I have a great gym but can't afford a personal trainer. What are some things to do to strength train or websites w workouts I can learn?

Maybe check out your local public library and see if they have some DVD's on this. I have seen them there in the past. Or go online and buy a cheap (used even) DVD to find one that will guide you through it correctly.

To start out, major compound lifts. There's no reason for isolation movements like targeting biceps or triceps etc. The only isolation that's really acceptable is for the legs since the muscle groups are huge, quads, hams, and calves. If your gym has machine weights, work chest, shoulders, back and abs. Doing this will get all minor muscle groups hit while targeting larger muscle groups. In the far future, if you feel the need to target specific areas for aesthetic reasons, do so, but not until you've got a solid core plan in place and have milked all of the "beginner gains" first. Youtube is your friend as well, there are millions of example programs out there. Starting Strength, 5/3/1, are both good programs for beginners.