How to get to the third gym?

To get to the 3rd gym you need the HM01 (Cut). To get cut you need to get it from the captain of the S.S. Anne. Here are the steps to get it:

Step 1:
Go on the S.S. Anne and go left up the stairs.

Step 2:
Go down the hallway, make a right, make a sharp turn upward. (Rival) will come down from the stairs and challenge you. Beat him.

Step 3:
Go up stairs and talk to the captain. After a nice back-rub, he will give you HM01.

Note 1: It would be a smart idea to challenge the trainers in each room. Not only will you get Experience, but you will also get some items.

Note 2: When you walk into the S.S. Anne, the second room to the right has a girl in it. That girl will heal your Pokemon whenever you need it.

Hope this helps!

-Hero412 ;)