Creating your own website is easier than you think. All you need is a domain name, a reputable hosting service, and some easy-to-use software for building websites.
Finding the right domain for your new website is in some ways the hardest part of the job! Essentially, you have to decide if you're trying to build a brand with your website (in which case your domain name should be unique or memorable) or whether you're going after searchers (in which case your domain name should incorporate a good keyword). The two approaches are very different.
Don't underestimate the time it will take to do this. It's not technically hard, but it can certainly be challenging. Be prepared to spend a lot of time to come up with the perfect domain name for your site.
Don't forget to register the domain name as soon as you find it. Use a registrar like GoDaddy, NameCheap or 1&1. Don't use their hosting services, though — keep the domain name registration separate from the web hosting.
Once you've registered your domain name, it's time to find yourself a reputable website hosting service. Don't go just on price, look carefully at the features that are available.
Finding a hosting service provider can seem a bit overwhelming given all the choices that are available. You'll want to start with a simple Linux-based shared hosting service, by far the most common service available. Look for a provider that includes some kind of "control panel" support (cPanel is popular choice) to make managing the website easier.
If you think you'll be creating more than one or two websites, consider getting yourself a reseller account. Reseller accounts let you host multiple sites at a low cost, definitely worth investigating.
The last thing you need is software for building websites. A good site builder is essential for creating and maintaining your website.
Professionals use top-of-the-line builders like DreamWeaver, but they're overkill for someone just starting out. There are free or low-cost site builders available if you do a bit of searching. Your hosting provider may even offer one as part of the hosting package.
Expect to have to learn some basic Web terminology no matter what site builder you're using. Learn about HTML and CSS as a minimum, because they're the core technologies used to build websites.