Confused about flying for the first time

Hi, I will be flying domestically in the United States for the first time, and I am wondering how luggage will be transported. I am bringing a suitcase(Not carry-on) with me and I want to know ahead of time what I need to do. If it helps, I will be flying on two separate planes under one ticket from CLE to ORD, then ORD to CMX. Will I need to grab my bag once I land at the first stop? Whats the procedure like?