For cleaning your screen, you should use a damp (with water) soft cloth to wipe away whatever is on your monitor. This may take several repeats, but should clean your monitor just fine. Be careful to avoid dripping water down the screen; this is a wiping procedure, not a washing...
When you are done, use a dry cloth to dry the monitor right away. Never spray cleaning fluid directly onto the monitor, as it can damage the monitor and other computer components. If you have a LCD monitor, the process to clean it is slightly different because the screen is more fragile...