How do you stop the drain valve of a hot water heater from dripping. Is it safe to put a cap on it?

No dont even think about putting a cap on it, its dripping for a reason, call a plumber to fix it, a hot water heater is a dangerous appliance and should not be dealt with lightly.

If you have a drip, but can't fix it or get a plumber out right away, use a garden hose to route the water to a drain nearby. Most drain valves are threaded with garden hose fittings.