Get organizedI'm a "to do" list guy. Everything I do on a daily basis centers around "to do" lists. Whenever I think to myself, "I need to..." it goes straight on to the list. For these two projects I used Ta-da Lists. I created a new list for each project, and started adding "to do" items as I thought of them, and checked them off as I completed them. It's a great way to ensure you don't forget anything, nothing falls through the cracks, and it gives you a decent visual representation of your progress and how much you have left to do.
Get a domainThe first thing you need is a domain name for your site so people have a way to surf to it. You don't necessarily need a separate domain for every site; you can can host several sites on a single domain via sub-domains. For example, I registered anachromystic.com for my company then hosted one of my projects at marina.anachromystic.com.
I get all my domain names through GoDaddy. It's usually the cheapest, and it's convenient to manage them all through a single central service. If you plan on sending/receiving e-mail through the domain, I strongly recommend Google Apps for Business. It's dirt simple to set up, their tutorials cover every major registrar, and requires no maintenance.
Get a hostAs the name "pet" project implies, these sites are hobbies. They are not generating any money, and it's not critical that they be up all the time and fast to respond. So I went with the cheapest host I could find, DreamHost. Pull up Google and search for DreamHost promo codes and try all the ones you find. I ended up getting an entire year of hosting for about $20 (that's for the entire year, not a monthly rate).
Choose a platform (Hint: Use Rails, dummy)Not only is Ruby on Rails the best platform for getting a site up and running quickly, you can get a head start with a "base" application like Bort which comes with a plethora of pre-shaved yaks including registration, e-mail activation, log-in, password reset, pre-configured routes, deployment scripts, etc. It's not perfect - I had to tweak it a bit - but it saved me hours of laying the groundwork and let me get to the meat of the project quicker.
Use hosted source controlWhy hosted? First of all, it's essentially a cheap back-up of your work. Secondly, it makes it a lot easier to collaborate if you're working with other developers. There's a billion to choose from, and if you're willing to let other people see your code, they're free. I decided to make the source for Pocket Rails open but keep the source for Marina private (for now). I'm a huge git fanboy so GitHub was the natural choice for me. My open-sourced projects are hosted for free and I pay a measly $7 per month for the privilege of keeping some of them private.
Test all the fscking timeIf you aren't test infected yet, it's time to wake up. Testing demonstrates that what you've written works, and testing ensures that when you modify or enhance it you don't break any of the old stuff. Don't let yourself fall into the quagmire of, "I'll add testing later after I get everything working." You'll waste endless hours of debugging issues that could have been prevented with preemptive testing. But don't take my word for it, take the word of Bryan Liles.
Also, on a somewhat related note to testing, use one of the plug-ins and accompanying services like Hoptoad or Exceptional to track and alert you when something breaks on your site.
If you want to get hard core, and why not, install the New Relic plug-in which will track and report on the performance of your application, so you can find out where the bottlenecks are.