Each creature that starts its turn in the webs or that enters them during its turn must make a Dexterity saving throw.
I believe that this means that if you are not in the webs and enter them, you must make a save. If you succeeded, exited the webs, and re-entered them, you would have to make another save, as you are "entering the webs during your turn".
Unlike many other spells such as moonbeam, web does not state that the save occurs only the first time you enter them.
Do you have to make a save for each square of webbing that you enter?