I was doing the dishes the other day and the cold water went out. I can get Hot water, but not cold at the kitchen sink. I checked the nobs below the sink and the cold has a leak coming from the nozzle. Any help would be great.

Thanks

That "nob" is called a angle stop. The "nozzle" is called the stem.
Open the angle stop up a little way until it starts to leak . Now snug up the nut on the stem until the leak stops.
As for your faucet it sounds like some crud got sucked up in the inlet ports of the cartridge and are now blocking them. Shut the water off at the stops, pull the cartridge and check and clean the ports. To tell you more I will need the brand name of the valve and about how old it is. Good luck, Tom