Today the kitchen faucet stopped shutting off completely. Its not dripping it's a steady stream of water. Don't know the make or model of faucet just a generic single handle and the house was built in 1954.

With the brief info you gave can't help much. Could be any number of faucets with different cartridges. Foe now, turn the water off under the sink. With that age, just replace it.

After you shut off the water supply and confirm there is no pressure you should be able to unscrew the valve body to get at the cartridge. https://www.youtube.com/watch?v=1h1JE0ygcIo

Post a picture of it. We will identify it for you

Milo