Single lever faucet... would be great to have a name or maybe you could post a picture of valve under the "go advanced" feature at posting box. If can get name or a pic. To us we may be able to get you a specification sheet on your specific valve... make getting removal/replacement of parts easier.
Anyway, yes... need to shut water off to work on shower valve. If valve on 1st floor, look in basement for shutoffs that go directly to shower valve, if on 2nd floor, look behind tub and see if access panel there... if access panel present, remove and should see 2 shutoffs. If can't find shutoffs that isolate the valve, then shut the main water shutoff at the water meter OFF.
Then, remove handle and valve cover plate and will probably see a large brass nut or a cartridge with a chrome clip... idea here is that you will need to loosen the brass nut, or remove the clip, and then remove the cartridge assembly to investigate this issue.
Most likely cartridge needs to be replaced... hot/cold water lines will need to be flushed (just a quick pulse of water to clear the lines of any sediment, etc.), and then valve needs to be reassembled.
Anyway, that is basic breakdown. See if can get us name of valve or a picture.. see if we can do better than this...
Let us know... Mark