Morning engines checks - like ones you don't do on your car - can be carried out by crew - to help them remember what to look at use the mnemonic - WOBBLEE

Water - check the raw-water strainer. Look for water and no weed
Oil  - wipe the dip-stick and redip. Check level is between the marked and condition of the oil.  Milky -water in the sytem. Black - you need an oil change
Belt(s) - check the tension of the drive belt, you should be able to twist no more than half turn /deflect by 1/2 inch.
Bilges - look forward discharge: red - coolant/diesel, clear - water, brown - oil.
Look/Level - a general look round but also check of the coolant levels
Electrical connections
Exhaust Water - after engine has started check for water coming out with the exhaust gases