Depends on what format the icon came in, and what type of file/program you are applying the new icon to, there are different procedures.
Now the icon could come in folder format, icn file, or just a png file.
In folder format you basically get a folder, with the icon already applied, you can copy it from "Get Info" window and paste to another "Get Info" window, this will work for folders and files, but not well for apps.
icn file are mostly for apps only, to apply you control or right click the app and select open package, go to Contents/Resources/ folder and replace the original icn file with the new one, after you back it up.
png file are just a raw image, you need other program to convert it into icon with all smaller sizes.
If this sounds confusing, there are tools that will accept all these formats and streamline the process. Check CandyBar (
http://www.panic.com/candybar/) it's a really easy to use shareware, trial available. And if you collect icons, check Pixadex too (
http://iconfactory.com/software/pixadex/).
one more link on ICN:
http://www.iheartny.com/howto_03.html