Shoving isn't exactly new to D&D 5e, it is a base ability, and as others have pointed out it requires one of your available attack actions to shove normally, and in the base game it is a contested check. This means you use your Athletics + a 1d20 versus the one being shoved also using Atheltics + 1d20. Unlike attack rolls though if you both get the same number on a contested check it is considered a failure, or nothing happens.
