Can someone give me a rundown on how to use FTP?

FTP stands for File Transfer Protocol and it is basically a means of connecting to your web server w/o logging into your host's control panel. I find it much quicker because it acts much like copying files from one window to another on your computer. In the host's control panel, there is a file upload system, but it typically only allows a few files to be uploaded at a time. With a FTP client, you can drag many files from your folder to the server folder and it will go through the list and upload them all. It's really convenient.

Not all free web hosts offer FTP, but the good ones do. Upon registering, they'll typically assign you a FTP user and password. If not, check your host's control panel. Paid web hosts allow you to setup the FTP account yourself within the control panel. Once you got the FTP account and password, you use those credentials in a FTP client. The client I use is the Firefox 3 add-on called FireFTP. You'll find a link in the Free Software sticky. Another popular one is FireZilla.

And how would you add stuff like smilies and skins?

It depends on your forum software. Some may allow you to upload them directly via the system's ACP. Other systems require you to manually upload the images and then connect them as emoticons or skins via the ACP. Based on your other post, I believe you're using phpBB 3, so your emoticons go inside the /images/smilies folder and templates go in the /styles folder. These are relative to the phpBB root folder.

After the files have been added, go to the appropriate section in the ACP and set them up. For emoticons: Posting tab > Smilies. For styles: Styles tab > Install: The style you want to install.