First of all, if the engine has a handcrank, then turn the engine over by hand to ensure that the pistonsand everything else is freely moving. Check the fuel filters and make sure there is no major blockage in this area. Check your oil levels. Make sure you have lots of fuel in the fuel tank. Batteries are fully charged and that the electrics are for starting the engine and properly connected and secured. If the boat is out of the water ensure that you plenty of water for the engine(the water inlet hose is in a bucket of water and that there is lots of water to replace what is being drawn into the engine) If the engine is fresh water cooled( closed cooling system make sure that there is plenty of coolant in the system.
If everything checks out and is ready, you should be able to start the engine. But before you do, just turn it over for a few seconds without any throttle on. This will loosen the engine up a little better than just using a hand crank earlier. If it has a glow plug, then turn this on, wait the a few seconds, and start the engine as per the manufacturers recommendations.
It probably won't start right away. If it doesn't wait a minute or so and try again. When it starts, it may stumble a bit, but should settle down once it starts to warm up. Check the exhaust for water. There should be water coming out of the exhaust. It shouldn't be a dribble. It may pulse a bit but that is fine. Once the engine is running ok, check that she is charging your batteries. You may want to let the engine run for a period of time to get to close to operating temperature. After which, when the engine cools down a bit, you can change the oil and oil filter. That is the essentially it.
Nigel Calders book Mechanical & Electrical Handbook for boats is an excellent resource.