You want this kind of thing, it easily removes the hair that is clogging the drain.
https://www.lowes.com/pd/FlexiSnake-Plastic-Drain-Stick/50257883
The difficult part can be the drain cover. You need to remove it because the hair plug will be sizeable and can’t just be pulled through the holes that the thing fits into.
Same thing with sinks in the bathroom btw, it is always hair and it will stink horribly, so be prepared for that.
It isn’t clear if it is draining slowly. You need something to physically remove the obstruction and something like this works really well for hair and might work for fatty stuff in a kitchen sink.
https://www.lowes.com/pd/FlexiSnake-Plastic-Drain-Stick/50257883
If it doesn’t work, at least it was cheap.