1) Ask questions from people who seem like they know what they're doing. You can identify them not from how much they lift or what sort of faces and noises they make, but from the smoothness and fluidity of their motions. Someone who makes slow, even, controlled motions is a good sign. If you go the personal trainer route, ask him/her to demonstrate each move. If you don't see that sort of control, take everything that one says to you with a grain of salt. Most people at the gym, even the non-trainers, will not be bothered by someone asking between sets how to do one particular exercise. Just be polite, direct, and probably ask someone who doesn't have headphones on.
2) Don't try to start too big. Pick a small number of exercises at first, and learn completely how to do them. For example, if you want to do a push up...is your back straight? Are your legs in line with your back? Where do you put your hands? What direction do your elbows bend? How far should you lower yourself? It's better to get these questions answered and do 10 of them perfectly than to do 40 half-assed. You might try something like a push up or bench press, a chin up or pull up, and a squat or lunge to start. Master how to do your basic group before expanding outward. The same goes for the weight you use. Start small, make sure you're doing it right, and then add a bit more weight, or another rep, or drop the reps by a few and add another set.
3) Consider trying to do some things that don't require a huge amount of instruction or equipment. Running intervals--that is, doing a bust of high speed for like 30 seconds, followed by about 90 seconds of a slower jog, then back to the sprint, etc, for about 7 cycles--is actually pretty good for both your cardio health and for fat burning potential. So is jumping rope.
4) Make a large number of small, realistic, incremental goals for yourself. Don't think you'll start out running three miles a day; think you'll do 2, 20 minute cardio sessions a week in your first two weeks, 3 in your next two, 2 30 minute sessions in the next, and so on. Increase your time, frequency, and intensity gradually. If you can do 20 perfect form pushups today, aim for 21 in a couple of days. It's great to have some long term goals as well--I'm still working on trying to get to that 6 minute mile I set as a goal earlier this year--but I, at least, notice progress more easily when I can note, for instance, that today's run was indeed 0.1mph faster than last week's, or it lasted a quarter of a mile longer while maintain the same pace, or the like.
5) To echo a previous comment--consider starting with the machines to learn the basic motions and figure out what your limits are, and then later move to the free weights.
Learn to recognize different sorts of pain and tiredness--stabbing pains are bad and probably mean you've either injured yourself or are doing something wrong, while dull aches just a sign of general muscle fatigue. While you want to push your limitations, you want to do so in a sustainable fashion, not one that will cripple you or cause you to faint. Ultimately, be skeptical of advice that claims it will completely transform you in 6 weeks, or promises you'll look like the unrealistic and possibly airbrushed cover model in 10 minutes a day. A lot of magazines will make outrageous claims this month, only to try to sell you an entirely different set of exercises next month, and a different set from that the month after that. Instead of going for a complicated fad, go for the tried-and-true method of simply working out regularly, each time a little bit harder, a little bit faster, a little bit more weight than the last one.