So I've seen a video that explains the basics of the level editor, and a pdf that completely explains building a level, except for adding sounds. As of right now, I have no idea how to add ambient sounds or music to a custom level. Can anyone tell me what I have to do? I want to learn this before I get the game so I can jump right in and make my own levels.

I forgot about adding objectives and a briefing. How do I do those things?

I think the answer lies here, I found this wiki earlier today. On this page in particular there's explanation concerning sound and music, and how it works a little different than it normally does in UnrealEd that comes with other Unreal Engine powered games. http://induktio.net/wiki/Adding_sounds_and_objectives

There's a mod which you can download there, "Ambient Sound Mod 1.0", which lets you use sounds from other stock maps in your custom map. It consists of "SoundEffects.ini" file, which normally resides within "\SWAT 4\Content\System\" directory, but the edited one from that mod has several entries removed.
I'm gonna give it a try later.