If you are in the middle of a toilet repair and are waiting for the toilet handle to arrive, here is how to flush the toilet without the handle.
Step 1 - Remove the Tank Lid
Take the lid off of the toilet tank to access the internal parts. You should see the tank full of water with the tubes that come from the water supply behind the toilet attached to the float ball on top of the water. The float ball is connected by a chain or rod to the rubber flap at the bottom of the tank, covering the hole where the water enters the toilet bowl when you flush.
Step 2 - Take Precautions
The water in the tank is clean, but if you wish, wear a pair of gloves for protection.
Step 3 - Pull the Flap
Press down on the toilet handle to lift the rubber flap from the hole, thus allowing the water in the tank to rush into the toilet bowl. Since there is no handle you must reach into the tank water and manually lift up the rubber flap. The toilet will flush as normal and the rubber flap should return to its original place over the hole on its own. The tank should fill with water again.