How can I add a ThirdParty library so that it compiles when I compile my game?

Did you see this ? UE3 Wiki - Linking Static Libraries Using The Build System ?

I followed that, digged a bit into my Build.cs and found it worked really well.

If afterwards you still have issues , please specify which part and I’ll try to help.
There is also already a ton of similar questions in this AnswerHub , i.e. here