Usually the most of sailing boats and the most yachts have an auxiliary diesel engine to allow you to more easily maneuvering in marinas and allow you to keep moving if the wind stops blowing.
If you don't do the regularly services and undertake some basic daily checks it will take that opportunity to breakdown. These checks are simple and you must be sure that can be undertaken when the engine is stopped. You can isolate the batteries first before working on the engine. You must keep on mind that batteries must be changed every two years, depends of the use ,of course .
Check the water coolant level in the radiator and also check the raw water strainer to make sure it is not blocked.
Check the oil level in the engine and gearbox by using the dip sticks.
Check the alternator belt is not damaged or too loose or tight.
Check the bilges for oil or water. If there is water or oil check from where it comes from.
Check for leaks around the sea cocks and on the fuel lines.
Check that all electrical cables are connected and check if the wires is in good order.
Check your fuel tanks, if they are full enough .
Unisolate the engine battery after closing and securing the engine cover.
Now you can start the engine. Make sure that you can see the sea water is pumping through the coolant system and exiting from the exhaust. Leave your engine run for a few minutes before you set your lines to leave.
Have a nice trip !