Residential hot water systems normally supply both hot and cold water based on the pressure of the cold water coming into the house. The procedure for working on hot or cold is pretty much the same:
- Turn off the house shutoff valve (which by definition is cold water)
- Open faucet(s) to drain water/release pressure.
If your hot water heater is downstairs and you are working above it (the floor above or the pipe you are working on is higher than the output of the hot water heater) then this is pretty straightforward. If you are working on pipes below the hot water heater output then you will effectively be draining part (or all) of the hot water heater in the process, but I don't see any way around that.
If you will be (effectively) draining the hot water heater then I recommend turning it off before you get started (turn off the gas or flip the breaker) to avoid any problems that might be caused by letting it heat a less than full tank. Keep in mind that older gas water heaters use a pilot light, so restarting them is NOT as simple as "turn on the gas".
Slight modification for your setup: If you have (which I think you said you have) a cold water shutoff on the input to the hot water heater and you are ONLY working on hot water pipes, you can use that shutoff valve instead of the house shutoff valve. That has the advantage that you will continue to have cold water in the house while working on the hot water pipes. However, you still need to open faucets (just hot water) to drain water/release pressure before you start working, and the warning about possibly turning off your hot water heater still applies. But as Tyson pointed out, this is not foolproof and using the house cutoff may still be a good idea.