You can use the inclined bench, or a flat bench and lie down.
Do a variety of lifts - eg 10 of each.
Arms by your sides, bend at the elbow, bring weight up to shoulder and straighten arm again (this will work the muscle down the front of the upper arm).
You can also work biceps by using the barbell or the 'preacher curl' (where you sit and have your arms supported over the frame in front of you)
Hold weights straight up in front of you. Bend the elbows so that the weights come down beside your ears and lift back up again -this will work triceps (the big muscle down the back of the upper arm).
Hold arms straight up in front of you with weights touching. Keep your arms straight and move hands/weights out to the side and back. This is quite hard so build up the reps slowly or you'll have aching shoulders and upper arms.
Do 5-10 to start with and build up the reps very carefully and slowly because this will work your muscles HARD! Don't let your arms drop below the level of the bench - if you do this you have to start the lift from an angle that puts too much pressure on your shoulder in its weakest position.
Arms straight and held down by sides, keep straight and lift weights out to the side to shoulder level and back (slowly). Again, don't let the weights go backwards and 'below' your body.
Best in a lying/semi-lying position) - rest one arm on your thigh, have the other arm straight holding weight. Start to turn circles and increase diameter until you're stretching as far as you can.
Reverse the direction and decrease the diameter back to the starting position. The trick is to keep your arm straight and gradually move the weight in a bigger and bigger arc - at the end you should be reaching right out to the side, right above your head, right across your body, and down towards your feet. When you can't get any bigger, then reverse the movement, make smaller circles and come back to rest with your arm straight up in the air.
This can be done with both arms moving in the same direction, or with an alternate arm swing (as in back stroke swimming). Arms straight, weight in either hand.
Reach up above your head and then swing weights down to hip level - get a good stretch above your head. To do alternate swings, start off with one weight above your head and the other at hip level - bring one arm down and the other up at the same time in a good steady swing.
If you're standing do the following
Lifts to the ceiling - start with weights on your shoulders and straighten arms upwards
Arms by your sides and lift upwards with a straight arm until arms are horizontal at shoulder height
Hold weights together on upper chest. Keep the weights touching and straighten arms forwards, then come back to chest again. Keep arms parallel to floor and don't allow them to drop.
Start with arms straight ahead in front of body, weights touching. Keeping arms at shoulder height move out to the side until arms are in the same plane as the body (move backwards through 90 degrees). Keep arms straight and don't allow them to drop down and return to starting position.
Stand with one foot ahead of the other. Rest one hand (and weight) on thigh of forwards leg. Keep facing forwards, don't twist body, and lift other arm (plus weight!) backwards until it is parallel to the ground. Bend and straighten the elbow, keeping the upper arm still. Don't allow the arm to drop downwards. Repeat with both arms.
Don't try to do all four movements at once or you'll have sore shoulders! Do one or two, go to another piece of equipment, and then come back for more, that way you'll reduce the injury risk.
Start with a lighter weight - beginning with a heavy weight is a good way to get a shoulder injury. When a weight is in your hand at the end of your arm it also effectively weighs 'more' than when held close to your body, so work up to higher weights.