I’m really fuzzy about how naval movement works. I’m just not getting it.
The side that has initiative on that front gets to move its ships first.
Each ship has a movement of 10 spaces, but each ship must also use that movement range to return to the port it started from.
Once you decide what ships you are moving, and to where, you declare what space you intend to patrol, if any. (By patrolling a space, you are saying that you intend to do combat with any ships that are found in that space.)
Now the other side moves its ships. They go about it the same way as you did, but they obviously have seen where your ships are. If the other side patrols the same space as you, then there will be combat.