Does the gym have a stationary bike, spinning bike (whatever it's called), or a rowing machine?
Here's the link for the workout generator (to come up with a strength training routine): www.sparkpeople.com/resource/fitness_plan_
Play around with it and find something you like. You may want to start out with the machines to get used to the idea of strength training. If the gym has a cable cross machine, try it out. When I was doing my strength training at the gym (before deciding to use my bodyweight and dumbbells), I found that I liked the cable cross because I was able to do a full body strength training workout on it (excluding the abs). Also, don't be afraid to consider doing body weight exercises (which may be better than using the machines).
Also, if the gym has a personal trainer. If so, consider getting a personal trainer. They could help you come up with a plan. Does the gym offer any classes? If so, see if any of the classes focus on strength training. Some gyms may have classes that focus on learning about bodyweight exercises, dumbbells, medicine balls, etc. or focusing on strengthening the core. If the gym doesn't offer courses like that, mention it to them. Maybe they could find out if other members would be interested in similar programs and get something started.