Finding the language generated by a context-free grammar
Hint: What can you say about the number of $a$s and $b$s in the produced words?


  It would be very helpful if someone were able to provide some tips on
  solving these sorts of problems.


There is no one-size-fits-all recipe here. It is undecidable in general, whether two CFGs produce the same language or two CFLs are the same language. A useful method is trying to notice the properties which remain invariant during the productions.