I've heard of FTP but I'm not exactly sure how to use it. What's the best way to get pages from my computer to the server?
FTP stands for File Transfer Protocol. It provides a method for passing bulk data to a server. There are a number of tools available that you can use to perform FTP uploads to your hosting provider. A popular choice is FileZilla - a free open source FTP program which has fairly good documentation and is available across most popular platforms.
It's important to keep a few things in mind when using FTP - it is not encrypted by default meaning your credentials and content that you send are sent in the clear so are vulnerable to interception. To address this you should connect to your hosting provider using FTPS (FTP over SSL/TLS).
Your hosting provider should be able to provide you details with the address for connection for FTP upload and on what credentials you should use to connect.
Depending your hosting provider, and how you build your website there are a number of tools out there.
As Wolfwyrd explains, you could indeed use tools like FileZilla to upload your files manually.
Other programmes such as the Visual Studio family (right down to the recently released WebMatrix edition) and Dreamweaver include mechanisms that allow you to "publish" your site to a hosting provider - under hood however, these will all be using FTP to transfer the files to the server.