It's easier than ever to get published. As Seth Godin would say, you just need to choose yourself - just decide you want to be a published writer, and boom you can be published.
It really is that simple these days. It doesn't take anything fancy to start a blog, and it really doesn't take much to get a least a bit of traction.
I personally started blogging years back as a project in college, with a humble WordPress.com blog. I then added a domain to said blog, moved the blog to WordPress running on my own hosting account, moved to another web host, then another, then moved my site to Kirby CMS, and finally on to my current web host. In the mean time, my blog was the catalyst behind every job I've gotten so far, and has earned a decent chunk of change - nothing to supplement my real job, but enough for a couple nights out a month, and server costs.
Here's what you need:
A domain name
The very first thing you should get is a domain name. Any domain name, really, but ideally something you can live with for years, decades even. Your domain name is the only online identity you really own, and if you start blogging with your own domain name, you can move your site to any other service and your old links and followers will still be able to keep up with your site. No matter where you're going to start a blog, getting a domain name should be the first order of business.
Domains aren't free, but at $10/year on average, they're not very expensive either. I'd recommend registering your domain at a different company than where you're hosting your site, so your domain can never be locked up in a dispute over your hosting, or vise versa.
There's a number of places to get a domain name. I'm currently using Namecheap, though Gandi is another place that I've often seen recommended. I also have domains with Dreamhost, and have bought a domain with Media Temple before; both can be fine options, but I'd again recommended using a different place to register your domain than you're using to host your site.
Also, I'd recommend getting a .com domain name. There's no reason you have to get a .com, but I'd still highly recommend it, since most people will assume it's a .com by default. It just makes things easier.
One more thing: never get rid of that domain if you've got any bit of traffic coming to it. If you want to switch to a new domain, point the old domain at the new site, but don't just throw it away.
Social Media
Now run, don't walk, and get at least a Facebook Page and Twitter account for your site. An App.net account - especially now that they have a free tier - might be a good idea too, as would a YouTube or Vimeo profile. But at the very least, get a Facebook Page and Twitter account. Try your hardest to get the same name as your domain, but if you must, settle for something different. Just make sure to get the very same name on both accounts, even if it's not the same as your domain.
A Place For Your Blog
Wait: give yourself a round of applause. You've gotten halfway there already. Because now, no matter where you put your blog, and no matter what you change in the future, you can always get your site followers pointed to your current site.
You're now ready to start your blog. There's a number of options of how you could do this, and here's the services I'd recommend:
Hosted Services
The simplest way is to just use one of the ready-made blog solutions online. They're free, work great, and you can always move on to something else if you need to, now that you have your own domain. You won't be able to change as much, but you won't have to deal with hosting, either, which is a major bonus. Here's the services I'd recommend:
WordPress.com - This is where I first started my site, and it'd still - for most purposes - be the place I'd recommend. You'll need to pay to bring your own domain, and you'll need to pay to tweak your site's theme beyond the basics, but otherwise, you'll have 99% of the power of WordPress without messing around with hosting. You can make a site with static pages, or just make a blog, and then can export your site to transfer your site to WordPress on your own server if you ever want to. WordPress powers many of the biggest blogs online, and it's the everything-plus-the-kitchen-sink option. And at least it's rather simple on WordPress.com.
Tumblr - Just want a blog, perhaps one where you quote and link to articles on other sites, share photos, and update regularly? Then Tumblr's a really great option. It's got less power than WordPress.com, but it's dead-simple to use, doesn't have ads, and has a rather awesome community. Bringing your own domain is free, and you can export your data easily, too. Plus, you can tweak your themes far more than you can in WordPress.com.
Skrivr - Want to try a new way to blog, something similar to Kirby like I'm using to power Techinch? A system where you can just write plain text files with Markdown formatting, sync via Dropbox, and publish without ever opening a browser window? Then Skrivr is the new blogging option you should try if you don't want to host your own site. It's simple, designed for writers, and the service I'd try if I was starting a new, free hosted blog today.
Squarespace - When you want to go pro, and don't mind spending a bit to do so, then Squarespace is the hosted service you should check into. You'll get some of the best site themes - and best visual site editor - on the market, great iOS apps, a solid service that even includes eCommerce support, and even lets you post from Dropbox. It's the only service I really considered moving Techinch to when hosting got to be too much of a pain.
Self-hosting Your Site
So you've outgrown Tumblr and WordPress.com, and want something more. That's the normal progression most bloggers make - myself included - and now you'll need to find the place to put your site and what to use to run it. But first, putting it online.
There's a few options out there.
Shared Hosting - You'll likely think of shared hosting first, but really, most shared hosts are awful. Sorry, but it's true. I've had terrible experiences with several, and even DreamHost went bad on me after a while. Media Temple's (gs) shared hosting has quite the bad reputation, despite MT's great reputation for their other hosting services.
There's two I think I can really recommend right now: NearlyFreeSpeech, which charges per gigabyte of storage and bandwidth you use, and A Small Orange, which has reasonably priced tiered hosting. A Small Orange is the hosting service Techinch is on right now, and it's working great so far. They told me via chat that they allow up to 512Mb of ram per shared hosting account, a limit no other shared host I've ever seen would share. I'd never trust a shared host that offers "unlimited" hosting, because they all have a limit. Somewhere.
VPS and Beyond - Shared hosting is nice because almost everything is setup for you, but the next step up - a VPS - is a great option that'll take a bit more work from you. You'll need to setup and maintain a Linux server, or get a managed VPS which is more expensive. Media Temple gets good ratings on their managed VPS, and VPS.net is a popular option for unmanaged and cheap VPS. Yet another option is a new app engine like Amazon EC2, Pagoda Box, Fortrabbit, or Heroku. They're very cool, but again, they'll take a bit more geekiness on your part.
The Software
Then, once you've got hosting, you'll need the software to run your site. There's more options that I could ever list, but the two solutions I'd recommend now are Kirby, the awesome plain-text CMS that I'm using on Techinch (see my full review for more info) and WordPress.org. If you go with WordPress, I recommend the Twenty whatever themes that come with WordPress, or anything from WooThemes.
You'll want a few other things: analytics to keep up with your site traffic, an email newsletter, perhaps, and ways to make money. For analytics, Google Analytics is still your best bet for a simple, powerful, and free analytics solution. Mint is awesome if you're hosting your site yourself and want to run your own analytics system. Then, MailChimp and its smaller and simpler cousin TinyLetter are both great for email newsletters. No reason to run your own email newsletter system unless you really want to.
You should also setup IFTTT to automatically publish everything you post to Twitter, Facebook, and any other social networks you use with your site. That way, your followers on those networks will keep up with what you write easily, without you having to remember to post to all of your sites.
You also might want your own customized email address for your shiny new domain name. Google Apps for domains isn't free anymore, for the most part, but you can still get 1 free email address on your own domain with it via Google App Engine. Here's a tutorial on how to do that.
Making Money
If you read this far, you surely want to get something out of blogging. Now, I never thought I'd make money - much less, a living - from blogging when I first started a WordPress.com blog, but my entire career has been shaped by blogging - and WordPress, incidentally - ever since.
The thing is, your blog can be successful, even financially, without actually making any money directly. It gives you a voice on the internet, lets people know about you and your work, and is about the best resumé you could ask for. Communications are always important, and if you can write well, you can express your thoughts about anything. That's a very important skill to show off.
Then, as you get a following, you have the chance to turn that attention into a business. You can write a book, or build an app, or record an album, and instantly have an audience for it, both on your site and your site's social network accounts. You can start a store on your blog, selling almost anything, and make some extra cash. You could start a paid email newsletter - yes, MailChimp supports that - or start a magazine app that's paid, and if you have people that love your writing, you'll get subscribers and make at least some money. You could even put a paywall on your site, and charge for some of your content, if you're successful. There's tons of opportunities, things that are making other people's incomes or at least some spare change.
But that's not all. Ads and affiliate links are another great way to make money, even while you're getting started. Ads are a tough nut to crack, though; they're based on pageviews, so you'll have to be successful at getting a lot of readers to make much there. Adsense can make your site rather ugly, and it really doesn't pay out that much if you don't have many visitors - and will only send you payments if you get over $100 in ad revenue. Not recommended, and yes, I've tried Adsense.
What I can recommend is trying to get into one of the newer, design-focused ad networks like Yoggrt, Fusion, or InfluAds, the ad network Techinch is a part of right now. You'll have to have a decent number of pageviews on your blog before you'll be able to be considered, but if you can get in, it's worth the wait. The ads look classy, are for stuff your readers might actually be interested in, and their payout if not huge is at least more consistent than Adsense.
But what makes even better money is affiliate links (just be sure to disclose that you're using them). Amazon famously has an affiliate program, as does Apple iTunes/App Store. Most companies have affiliate programs, which will give you, say, 5%+ from each sale made after someone clicked on the link in your article. Find an indie book or product that has an affiliate program, and it'll likely work even better for you. I'd recommend writing about stuff you'd write about anyhow, but if something does have an affiliate link and you'd write about it anyhow, then use it and disclose the use. You'll likely find yourself making money that way, if only enough to keep your server fees and domain name covered.
The most important thing, though, is trust. Don't sell yourself or your site out, and don't make your site a scammy mess of ads. It's just not worth it. Do your best work, without even thinking about how to make money from it, and it'll lead to more opportunities on its own. Really.
Write, and write, and write, and…
Now here's where I've gone wrong so much: you need to write often, at least every week if not every day. I'm bad at this, since my day job is editing Mac and Web AppStorm, and sometimes there's only so much you can write in a day. But the best way is to be consistent and write, even if only a little.
And have fun! Running a site is an adventure, and you'll keep learning from it. I sure have.