How do I replenish reserve sailors?

There are different types of replenishment.

First, your ships' crew quarters determine how many reserves can be on a ship while it's at sea and you can use those reserves to replenish when not in combat. If you run out of on-ship reserves, you'll see a red replenish icon and will need to return to port to get more sailors for that ship.

Second, the ports hold additional reserves for each ship. When you dock, the onboard reserves will be replenished from the port reserves.

Third, if you run out of port reserves, you can spend gems to replenish them. I believe it's 660 for the first, 1320 for the second, and higher again for a third and final replenishment.