In order to repair the boat, you will need two items: a gas canister and a propeller. These items can be found randomly inside any of the cabins strewn about the maps, but the propeller seems to have a slightly higher chance of spawning inside cabins near where the boat spawns. The propeller will be much more difficult to find than the gas, generally speaking, because only one will spawn in the map while three or more gas cans will spawn.
Once you have one of the pieces, bring it to the boat and hold A near the engine, you'll initiate a short minigame where you need to press either RB or LB when the meter reaches the highlighted sections; failing to press the right button will cause a delay but also makes the "sweet spot" larger. Characters with a higher intelligence will have both a faster-moving meter and larger sweet spots. Remember that you can not carry any weapons with you while holding a boat part, so you'll want to buddy up with someone to protect you in case Jason shows up.
Once the boat is running, the player not going for the achievement will want to get in with the A button, then hold A again to start the engine. A passenger can only board once the engine has started, and the boat can only hold one passenger (so two counselors total, including the driver). Beware, if Jason has the swim speed bonus, he will swim faster than the boat can move! If he reaches you, he will tip the boat over and cause both counselers to fall into the water.