A new water heater was installed yesterday, but I have no HOT water pressure in either of my showers. Is it the old fixtures, or a leaking pipes?

"Is it the old fixtures, or a leaking pipes?"
Neither one! When installing the new heater you disturbed the minerals built up in the pipe walls and turning on the valves sucked the mineral up and into the valve cartridge. The solution is to shut the water off to the shower valves and open them up and check and clean the inlet ports of the cartridges. Before you button them back up, open up the hot water line for a moment to flush out the line. Reassemble and test. Better now? Good luck, Tom

How do you do this?

dorimosher, it depends on which faucet you have