Do a couple of exercises for each body part.
Legs
Arms
Shoulders
Back
Chest
Abs
My favorites are squats, stiff legged deadlifts, calf raises, bb curls, skull crushers, DB curls, tricep pushdowns, BB military press, DB shoulder press, upright rows, shrugs,
Conventional deadlifts, Bent over rows, lat pulldowns or pullups, flat-incline-and decline bench press, crunches, and cable crunches. These are just my favorites, you may find that you like different ones.
you can split these up and do a couple of parts each day, one part per day, or just do a full body workout every 3 days or so.
I don't know what kind of equipment your gym has, but if it has free weights - they aren't as pretty as the fancy machines. However, used properly they are pretty darn effective. More effective than machines in my opinion.
As far as the actual machines you use, someone at the gym should show you what each macine is for and how to use it properly - that's what you pay for with the membership. Make sure to ask them. If you are interested in some free weight exercises there is a sticky in the beginners section with exercise descriptions and video clips of how they should be done. If that isn't helpful and you need a better description, just ask - one of us will try to describe it to the best of our ability.
Now don't forget, you aren't just building muscle - you have an entire body to work with - and that includes cardiovascular fitness so do some cardio work too (walking, running, biking, treadmill, whatever) - preferably not at exactly the same time as weights, some people actually do cardio and weights on different days.
Now for the most important part. Weight training and
cardiovascular training isn't much good without proper feeding. You will need to eat a protein rich diet with healthy fats and proper carbohydrates of the kind and amount that your body needs. Don't forget the green veggies, if you like things like breads and pastas - choose the whole wheat kinds.
That should get you started in the right direction. Please enjoy browsing the diet and nutrition stickies, weight training stickies, and feel free to ask any questions you may have.
Sorry if this comes a bit late. I got distracted in the middle of typing my response.