Most upper body exercises have as their goal to build strength. In order to maximize the beneficial effect of the routine, you'll want to mix in some good cardiovascular workouts - spinning, jogging, etc - and alternate the activities with lower body work.
Before starting any routine, be sure to spend at least 10 minutes warming up, including good stretching exercises. Warm, loose muscles are much less likely to tear themselves or attached tendons. Also, you'll want to get the circulatory system activated and muscle temperature increased for good blood flow.
How much weight to use, how many reps to perform and other variables are determined by your overall goals. Do you want to build muscle mass or just tone? For more mass, use more weight. For better tone, use less weight and do more reps. Do you want to increase flexibility and overall fitness or prepare for specific events?
In any case, these traditional exercises will help you get started down that road. Some can be performed without equipment, others require only a very simple set of free weights or resistance equipment. Resistance equipment includes rubber straps with handles, springs and others that work primarily by offering resistance to tension. Weights work primarily by providing compression and/or tension due to gravity.
Warning: Never exercise 'through the pain'. Mild discomfort - especially after a prolonged period of inactivity - is normal. But intense pain is a sign of trouble. Consult your physician.
Push-Ups
Even with all the contemporary sports science around, traditional push-ups remain an excellent upper body exercise. Start on your stomach, back straight, feet together, hands under the shoulders. Press against the floor, keeping your back and legs straight, then lower yourself back to the floor. For a little extra effort push-up, slow the action down and both raise and lower more slowly.
Try to do 20, then build up to 40, then to 80 push-ups.
More Chest Work
Start with 10 lb (4.5 kg) hand-held dumbbells. Flat on your back on a comfortable surface, such as a carpet or mat, hold the weights in each hand, palms up, arms extended perpendicular from the body. Lift slowly and bring the hands together.
To vary the action, and get the biceps a good workout, too, try bending at the elbow when the arms are raised about 20 degrees, then straighten and continue.
Lats
Stand up straight, arms at your side, grasping the dumbbells. Maintain good balance and breathe normally. At the maximum point of inhalation, thrust the arms away from the body, palms inward. Exhale as you raise your arms to shoulder height, then lower your hands slowly back to the starting position.
To vary the exercise, and get the biceps and triceps involved, rotate the weights and curl your arms up at the top of the swing. Straighten the arm, then lower as described above.
Do 10 reps.
(Note: The 'lats' or latissiumus dorsi' are the large, side muscles that make men triangle-shaped.)
Biceps and Triceps
Move the weights in front of the body, with your arms hanging above the front of your thighs. Without swinging or pushing off the thighs, lift the weights toward your chest. Alternate using one arm, then the other.
Do 10 reps for each arm. If you experience lower back pain during the exercise, stop immediately. Put off the exercise until another day, or see your physician.
Exercises for the lats or biceps can be done with free weights or using a long, elastic resistance strap. Hook one end with the foot and grab the other with your hand. Proceed as described above.
Pull-ups/Chin-ups
If you have access to a sturdy bar, either in the gym or at a playground, or at home in a doorway, you can perform chin-ups and pull-ups. Chins ups are done with the fingers toward you, pull-ups with the fingers facing away, while your hands grasp the bar above your head.
This low-tech exercise remains one of the best ways to build biceps, triceps, lats and pectorals all at once.
No matter what routine you choose, don't overdo it. Build up your strength gradually. One of the most common reasons people don't continue workouts is pain produced from incorrect technique or excessive effort exerted too early in the process.