The first step in determining the desired range of repetitions of each exercise is to determine your goals. Without having clear goals, the reps and weight used will be arbitrary. One your personal goal is determined, the repetition range to achieve that goal can be determined. Below is a general guideline for choosing your rep range.
Strength/Power: 1-5 repetitions
Growth/Tone: 6-12 repetitions
Muscular Endurance: 15+ repetitions
With the above guidelines, if your goal is to build and tone muscle, you would choose a weight that will allow you to get 6-12 repetitions with good form of a particular exercise. If your desire is to build raw power, choosing a weight which can be lifted 1-5 reps is ideal. If you are an endurance athlete or enjoy particular sports such as soccer, hockey etc. choosing a weight which you can lift 15+ reps is ideal.
One popular method for training the muscular system is the pyramid principle. With this principle, say for instance you're looking to build some muscle and shape your body, you would choose a weight you can lift with good form for 12 reps. You would take a little bit of a rest once the first set of 12 reps is finished. Add enough weight that you can complete 10 reps. you can then add even more weight and do a third set for 8 reps etc. It will take some trial and error to determine the correct weight used for each set of reps. I recommend using a "spotter" for safety.
Your fitness goal will determine your repetition range. Your repetition range will determine the weight used on an exercise. You know you have chosen the ideal weight for each rep range when the couple of reps you have to struggle to finish without sacrificing form. Those are the repetitions that will have you achieving your goal.
Most fitness centers offer free orientations to their members. During those orientations, many fitness trainers will demonstrate exercises and recommend specific repetition ranges according to your goals. I do very few of those appointments due to my schedule but when I do, I usually write up a full program for the member to follow. If you ask, I'm certain most trainers would be happy to do so as well. If you haven't scheduled an appointment, I encourage you to take advantage of it!