For those of you looking to do some weights, but not wanting to get into the whole "exercise every muscle" routine, the very best thing you can do is go back to basics.
The workout is very simple- bench press, squat and deadlift. These three lifts are enough to work your whole body. Those who train for strength (as opposed to body builders) tend to do these lifts only. Their triceps, deltoids, etc are just as developed as the body builders. What's hard about this is that these three basics can put a big strain on your body, but if you want a quick, easy-to-learn workout it's hard to beat. And when you're getting started, keep the weights well within your limits. Don't push too hard on these- concentrate on technique. If you're a beginner, one set of each will suffice to get you going. Keep the weights light and work in the 12 repetition range. Take your time, go through the motion of the lift fairly slowly, and keep it that way until you've mastered the technique. Go here for some tips on the deadlift.
Because there's not much to this, it's a good place to start and you can add it in to the end of your normal gym workout. When you've advanced a little you can switch over to doing three sets (I always include one set of light weights to warm up with and then do my three 'proper' sets) and gradually add on weight. Because these are compound exercises they work more than just the main muscle targeted and so you'll hopefully see muscle growth all over. Also, these exercises are fantastic for improving your strength, not just the size of your muscles. As always, take care and get advice from the gym staff on proper form- you'll not only save yourself from possible injury but you'll get much more benefit.