Loosen the propeller nut with a wrench or ratchet and then pull the propeller off the shaft and set it in a safe place.
Locate the propeller coupler, which is mounted to the boat's transmission. The propeller shaft extends from the coupler, which spins when the boat's transmission is engaged.
Loosen the set screw (or set screws) that are threaded through the coupler. Depending on your boat's propeller shaft setup, it may have one or two set screws. These screws are typically square-headed and are loosened with a crescent wrench.
Unlock the propeller shaft from the coupler with the propeller shaft key, if applicable, to your boat. Some boats have keys that are similar to Allen wrenches.
Apply a liberal dose of WD-40 to the area in which the propeller shaft meets the coupler. If the shaft has not been removed in several years, it may be rusted or otherwise stuck to the coupler. Once the first application of WD-40 has sunk into the joint, add more.
Pull the propeller shaft out of the housing. If it is still too tight to come out, add more WD-40 and allow the lubricant to soak in. If the shaft will still not come out, you will have to remove the coupler.
Loosen the bolts that mount the coupler onto the transmission. This will allow you to remove the coupler and propeller shaft together.
Put the coupler in a vise and try to pull the shaft free. If the shaft will still not break free, you may have to cut the coupler with an angle grinder. To do so, carefully cut two or more slots in the mounting area of the coupler until the shaft will break free. If you've had to go to this extreme to remove the shaft, you will have to replace the coupler itself. Before cutting into the coupler, ensure you can purchase a replacement coupler that fits both your boat and your price range.