To get a reward from the Ship, one or more of its parts has to be charged. When a part is charging, it is displayed on the Ship's icon in the game menu, on the Ship on the Map and the corresponding part in the Ship menu as highlight animation.
Tap the charged part in the Ship menu to get a reward.
You can also collect rewards from several charged parts at once. To do that, tap your Ship on the Map.
Your Ship is different from other ships on the Map because you can navigate it (tap a place on the Map to move it there), and it is marked by a circle.
To learn how much longer the part will be charging, tap this part on the Ship and open the Description window.