How to unclog a kitchen drain that has a garbage disposal?

I would expect that the offending matter is in the trap. All you need is a bucket and the trap should unscrew by hand. Should be an easy fix.

https://www.thespruce.com/repair-a-clogged-garbage-disposal-1824884

I'd pour some dish washing liquid down the drain, probably a cup, and let ti sit. That might do the trick.

If it doesn't then you can take the trap apart under the sink and clean it from there.

Pour baking soda down the drain. Then pour white vinegar. It will bubble. Add more vinegar if you have baking soda present. Let sit. Then flush with HOT water. Repeat as necessary.

Try some boiling water down both sides to loosen it up. Put baking soda down both sides, followed by vinegar. Let it fizz and bubble a while, follow this with boiling water down both sides and see if all this will loosen it to let it go down the pipes. If it doesn't, try Archie's suggestion of cleaning out the trap in case that is where it is stuck. If I put mashed down the disposal or sink, I always mix it with real hot water to thin it down to liquid consistency to keep it from going down in a lump.

I used a plunger when someone put too many potato peels in at once. Didn't hurt the drain or disposal

Thank you all for your suggestions!! The drain is now unclogged. I used many of the natural solutions: salt, boiling water, baking soda combined with vinegar, and dishwashing liquid. all combined, they didn't work. Before giving up and trying to take the trap apart (which I wasn't comfortable doing), I used a plunger. That worked!!! So, I'm not sure which of the prior solutions, or maybe the combination of them all, did the trick, but the plunger made it happen. I was thrilled!!! Thank you again!!