Here's the deal Eugene. The human body is an adaptation machine. Over time your body will get used to any training regimen that doesn't kill you, once that happens you will cease to get the steady gains that you experience when you first start a program. Weight training also is highly dependent on individual genetics. Everyone responds differently to training, and so a program that works great for one person might not be very effective for you. And finally, not everyone that trains with weights has the same goals. Some folks lift to promote maximum strength, some folks lift to increase their athletic performance in a specific sport, and some folks lift so that they look good naked

. That is why the corp of seasoned weight training afficionados here on this board won't give you a specific answer as to how many reps you should do in each set. The "correct" answer would require quite a bit of information about your current level of fitness, your body type, your fitness goals, and a whole pile of other variables.
However, the good news is that if you are new to weight lifting that almost any program you start will be effective. In fact, there are lots of scientific studies involving people that are new to weightlifting, and so we actually do have a good idea as to what actually works with people that are just starting out. Here's what I would suggest as an easy to use weight training program that will get you started. It's fairly easy to use, takes a minimum amount of time, and requires very little calculation. You will need to keep a detailed log of what you lift, but my experience is that people that won't keep a log of their workouts don't progress.
First of all, stick to the basic compound free-weight exercises like the bench press, the squat, the dead lift, the chin-up, etc. If you are a gym member you will be tempted to use the machines because they look "safer" and easier to use. They're not, and they aren't.
Second of all, don't kill yourself. The studies done with weight training newbies shows that beginners do nearly as well with one set of each exercise as they do with two, and that after two sets there is no added advantage. Advanced weightlifters often respond better to higher levels of volume, but beginners don't. Take time to learn the proper form of the exercises that you do, and make sure you work hard, but don't stick around the gym all day. Get in and get out, and then give your body time to recover.
Here's how it works. Each workout consists of five basic exercises. Use enough weight so that you can do between 6 and 10 reps. With the body weight exercises do as many reps as you can do. If it is less than five reps do another set after a bit of rest. Warm up a bit before your workout, and stretch afterwards. Split your workouts between your upper body and your lower body and abs. If you can do more than 12 reps with a weight then next time you do the same exercise add a bit more weight. Congratulations, you are making headway. On the body weight exercises you can either add a bit of weight, or you can add additional sets, whatever seems like it would be more "fun." Work out with weights at least twice a week, but don't work out more than four times a week (I would suggest three times a week.
Here's an example:
Monday - Upper body workout
Dumbbell Bench Press
Dips
Seated Dumbbell Raise
Chin-ups
Curls
Tuesday
Rest (Cardio?)
Wednesday - Lower body workout
Deadlifts
Lying Leg Curls
Hanging Leg Lifts
Crunches
Calf raises
Thursday
Rest (Cardio?)
Friday
Repeat Upper Body Workout
Saturday
Rest (Cardio?)
Sunday
Rest
Monday
Repeat Lower body workout
None of these workouts should take very long. In fact, the whole workout will probably take around 15 minutes. If it takes longer than that to drive to the gym you might want to consider simply purchasing a barbell some dumbbell handles and a bench and working out at home. Save the gym fees for later when you are interested in more advanced workouts.