Water barely comes out of my kitchen tap, then stops
Did you have any recent work performed on either the pipes, a hot water heater added, an Aqua therm unit installed  ?
Where are you located in the world ?

If so you might just have a piece of garbage in the aerators - at each faucet remove the aerators (thing at bottom of faucet outlet where water comes out you can unscrew it by hand usually) and then turn the water on. Then reinstall the aerators onto the faucets and test.
If you have copper pipes and sweating of copper joints was done - this is a very likely possibility.

Also as one commenter pointed out - frozen pipes ? - Both Hot and Cold ?