1. Read the questions carefully. There will always be enough information there, but you might need to read it a couple of times to get all of it.
2. Draw the triangles and mark in all known lengths and angles. You always need at least two pieces of information in order to find the third. You might need to use the fact that angles in a triangle add to . You might need to remember Pythagoras' Theorem. You might need to remember facts about angles formed by parallel lines cut by a traversal (e.g. X angles, F angles, Z angles).
3. There are numerous ways to remember the trigonometric ratios. "SOHCAHTOA" is the most commonly used.
Another that some of my students like is to look at the ratios like a set of three pictures...
The looks like a stick figure boy, and apparently "boys sin".
The looks like a stick figure girl, and apparently "girls get tans".
As for the third, if you're asked a question, you sometimes say "Ah, Cos" :P
4. Make sure your calculator is in the correct mode.
5. Avoid rounding off any answers until the very end. The sooner you round off, the bigger the roundoff errors will be.