Winterization is not just protecting your outboard against freezing, but should be a complete inspection and yearly service. I have watched the youtube videos, read the other answers, and none of them are complete, so here is a condensed version directly from Mercurys' service manuals.
You dont say whether you have a 2 or 4 stroke, carburated or fuel injected, the procedure is different. Let's deal with the 2 stroke first:
1. Clean the outboard with soap and water and a soft brush, and rinse with fresh water. If you have scale or marine growth, CLR or any similar product will remove this.
2. Sand and paint any nicks or scuffs in the finish.
3. Remove the propeller, inspect for fishing line or other debris around the propshaft. Grease the propshaft splines and replace the propeller.
4. Drain and replace the gear oil. Use Mercury high performance gear oil. If you have any signs of water intrusuion, have your gearcase pressure tested by a tech.
5. Inspect the power trim system and check fluid level.
6. Grease the pivot shaft and tilt tube, and inspect the steering link.
7. Fuel system and internal engine protection- Use Mercs' Quick-Stor to stabilize your remaining fuel and help protect the fuel system and crankcase portion of the powerhead. Mix the correct amount, 1 oz to 5 gallons of fuel, and run your outboard for 10 minutes at a high idle. If you have a DFI outboard, (Optimax) remove the fuel filter and add 2 oz in the cannister. DO NOT use spray fogging oil on any fuel injected outboard. Shut the outboard down, and drain the fuel system, including filters, lines, carburator. Remove the spark plugs, and spray each bore liberally with fogging oil, and rotate the engine by hand 2 or 3 revolutions.
8. Disconnect the battery, and store your outboard in an upright position, in a dry, well ventilated area.
Four strokes- follow the above procedures, plus:
1. Change the crankcase oil and filter.
2. Inspect the timing belt.
If you have a 4 stroke EFI, I would suggest you buy a service manual for your model, and follow the storage recommendations.
Before using the outboard in the spring, replace the spark plugs (if required), and replace the fuel filters.