WordPress is fairly easy to install manually, but many of the better hosting providers include one-click or other automated installation systems. These tend to work very well, so unless you really want to do it manually for the educational experience, I'd go ahead and use the automated system. When installing WordPress you can install in the root of your domain, a subdirectory or in a sub-domain.
Installing in the root directory
If you are using WordPress as a CMS for a new site installing in the root may be a good choice, but you could still use a subdirectory if you think you might want to do something else at the root level in the future. If, for example you install WordPress in http://www.yoursite.com/wordpress/ you can go into the control panel and tell WordPress what address to use and it will redirect links accordingly to the site shows up in your main domain anyway.
Installing in a subdirectory
If you are adding a blog or an additional site to an existing domain then it often makes sense to install WordPress in a subdirectory. I built heidicool.com in regular XHTML then installed WordPress into my blog directory to create my blog. When I created this site, I added it as a new installation in the samplewordpress subdirectory, as I felt it made sense from a marketing/branding perspective to keep it on my site rather than create a new domain for it. Note: Since I already had WordPress installed I could also have edited my blog installation to use WordPress's multi-site option and had the same end result. In this case I found it more convenient to keep them as separate installations.
Installing in a sub-domain
Generally speaking there is no particular advantage to using a sub-domain rather than a sub-directory, though search engine optimization folks can spend hours debating the differences. Sub-domains are, however, useful for adding blogs to existing sites. If you are hosting an existing site with a provider that doesn't offer good WordPress support you can create a sub-domain that you host with a different provider. Then just install WordPress on the new account and set it up so that your old provider uses the new one's DNS for the subdomain. (Or get a static IP address for the subdomain and have your existing DNS point to that.)
WordPress Installation Resources
- Download WordPress (only if you insist on a manual installation)
- WordPress Codex: Installing WordPress (only if you insist on a manual installation)
Installing WordPress on Dreamhost
As mentioned in hosting requirements, I use Dreamhost which has a very easy to use installation option explained in the video below. I've also installed WordPress on BlueHost and GoDaddy where the process is somewhat similar though GoDaddy takes ~30 minutes and is a bit clunkier.