Tennis elbow, or lateral epicondylitis, is a very painful condition on the outside of the elbow from an overuse injury. It can be caused from several sports or even overuse on your computer or iPad. These stretches and exercises should help.
The first set of exercises will loosen up the muscles, try not to push through pain, just get a slight stretch. You can prop your arm on a table and let your wrist hand off or you can hold it up in the air. Make a fist with your hand with your palm down. At your wrist, bend your wrist up to work the muscles in extension, and then bend it down to stretch the muscles in flexion. Then turn your fist to the side with the thumb toward the ceiling for a radial and ulnar deviation movement going up and down. Finally, with your palm open and your elbow by your side, turn your forearm up with the palm up in supination, and then turn it down into pronation. Do all of these about ten times.
Now for some exercises, you can use a soup can or resistive bands if you have some, but start off with something light. Go back to your flexion and extension movement, and go slow and controlled with this. Do about ten of these. Now grab a hammer or something that is top heavy to give you an extra stretch with overpressure. You will do your supination and pronation now with the hammer. Do ten of these.
For stretching, put your arm straight out in front of you. With your palm down, bend your wrist down with overpressure from your other hand. If this is not enough of a stretch, curl your fingers into a fist and do the same stretch. Hold these for 30 seconds, and do three of them.
Finally, roll up a towel and hold it straight out in front of you. Now you will twist at your wrist, like you are giving gas to a motorcycle. Try to keep the tension tight on the towel. You can also buy a Theraband Flexbar for more resistance.