How can I learn new moves and skills?

Once you get a Sync Pair, they'll usually come with 2 moves by default. You need to unlock the 3rd and 4th move manually, as well as the passive move for your Sync Pair.

In order to do this, press the Team Button and go to Moves & Skills. From here, you'll see which Sync Pairs you have that are capable of learning new moves, or your passive skills

The items that are required will depend on your Sync Pair's role. You'll need Training Machines, Buff Blends, Aid Ades, and Tech Tonics of varying rarities. You can view the requirements by clicking the skill, and looking at the list below them.

You should be able to get these items by completing the Story modes, or perhaps participating in different courses under the Training Area.