Brighten up the screen itself. Aim two lights with a total wattage between 500 and 1,000 watts at the screen at a 45-degree angle from either side. Make sure the light is even all around the screen, with no bright spots or noticeable shading.
Place your actor or actors in front of the screen where you want them to stand during filming. Don't place the actors so close to the screen that they create shadows on the screen. A clearance of 3 to 5 feet should provide enough room for the light on the screen to go behind the actor without a problem.
Light the actor or actors in the scene from the front with soft light that doesn't create a harsh glow. When properly lit, shadows disappear from the actors face and body, making the actor or actors appear more evenly lit. Use either soft lights on either side, facing in toward the actors at a 45-degree angle, or one soft light facing in at a 45-degree angle and a white bounce card, roughly the same size as the light fixture, facing in from the other side.
Use a backlight if any shadows appear on the green screen. Aim one backlight in at a 45-degree angle from one side. To prevent the light from interfering with filming, place the light a foot or more lower than camera-level and aim it slightly upward.