Most kitchen clogs are grease, and most of them clear with a plunger and ten minutes.
First — don't reach for chemical drain cleaner. It can damage the pipe, it often doesn't clear the blockage, and it turns the standing water into something hazardous for whoever opens that drain next. If you have already used some, tell us when you call. We can usually smell it, but we'd rather hear it from you.
What to try, in order.
Very hot tap water, run for a few minutes. Grease is the usual culprit and heat moves it.
A plunger. Use a cup plunger, and on a double sink block the other drain — otherwise you're just pushing water back and forth. Plunge firmly a dozen times.
Clear the P-trap. Put a bucket under the curved pipe below the sink, loosen the two slip nuts by hand, take it off and clean it out. This catches a surprising amount.
If there's a disposal. A hum with no spin means it's jammed — switch it off, put the hex key that came with it into the socket underneath, and work it back and forth. Nothing at all usually means the reset button on the bottom has tripped.
Why it keeps happening. Grease goes down liquid and sets solid further along. Coffee grounds, eggshells, rice and pasta all build up the same way. A disposal gives a false sense of security — fitting down the drain doesn't mean it reaches the treatment plant.
When to call us. Both basins backing up. Other fixtures in the house affected. Gurgling from another drain when this one runs. Or it clears and comes back within a few weeks — that means the problem is further down the line than a plunger reaches.