There a few different ways to install WordPress. You can either use WordPress for free on their domain (i.e. http://yourdomain.wordpress.com/), buy a domain right from WordPress and use the platform itself as your host (their rates tend to be higher than most hosting services, so this is very uncommon), or buy a domain and host somewhere else and install WordPress on it. If you opt to create your own domain with a separate host and install WordPress on your server, then you might want to check this out:
Things You Will Need
First, you will need to have a web host such as HostGator or WebsitePalace. Most web hosts will allow you to do this. It must have something called either Fantasico De Luxe or QuickInstall, or something equivalent that allows you to easily install a program such as WordPress with the click of a button. If not, you will have to upload it via FTP, or, in some cases, you won't be able to install it at all. If your host doesn't allow you to install WordPress (with FTP or otherwise); don't worry! Almost all hosts offer some kind of adequate blog service, and you can always transfer your files over to a more competent host.
Step 1Once you have either of these two open, on the left, there will be a button that says: "WordPress." Once you click on that, go to either "Continue" or "New installation," depending on which you use.
Step 2For QuickInstall, simply choose which domain you want to install WordPress on. Then, add what domain you want the blog to be at (i.e. http://yourdomain.com/blog/), your e-mail, and the title of the blog that you want to appear in the header and in the browser tab. If you want to have your blog as an extension of your website, then "/blog" is usually the best choice. If you want to have only a blog, simply leave it blank.
Step 3Fantastico is almost exactly the same. Again, choose the existing domain you want to install it on and what domain you want to create for it to be viewed on. Then, enter in your admin details, e-mail address, nickname, and your blog name and description.
WordPress is certainly a solid option for any blog, used by popular blogs such as TechCrunch and The New York Times. There are currently over 11 million blogs that self-host WordPress used by the process described above.
Tips & Warnings
Be aware, however, that your hosting provider may not have QuickInstall or Fantasico De Luxe, or something equivalent. In that case, you'll have to either upload it via FTP, or just use a different blog platform to host your blogs; almost all hosts come with some form of a blog service.