Tami - Is it on the disposal side? If so, take everything out from under the sink as it gets messy. Then put some plastic bags all under the sink. You can use newspaper but the water will be absorbed by the newspaper and leak through.

Now unscrew the pipes and let the junk drain out. You may have to unscrew the U shaped pipe at both joints to get it all cleaned out.

Once it is cleaned out, put it back together. Carefully take the plastic bags out from under the sink and do what you want with them. (I throw them away).

For us, pasta is notorious for doing this. I have since stopped putting any pasta in our disposal.