It's no secret that changing outboard motor and stern drive lower unit gear oil extends engine life. You'll need a long-handled slot-edge screwdriver, the jumbo shank to break loose the drain plug without burring its edges of the slot. Check gear oil a few hours after the outboard motor has been run to allow the emulsified water to separate from the oil. Barely crack the lower drain plug screw and see comes out, gearcase oil or water.
Even a scant few drops of water means you ought to check more often in case the problem gets worse. However, an ounce or more means a seal has failed. Undetected in its early stages, a leaking seal can cost hundreds of dollars to repair. But catch it early and oftentimes only the propeller shaft seals have to be changed, and not the expensive gears, shaft and bearing set. It's rare for the driveshaft or shift rod seals to fail, but it happens. Marine mechanics pinpoint exactly which seal is leaking with a pressure tester pictured in the foto above that pumps air into the gearcase.
The gearcase is dunked in the water. A trail of bubbles escaping from one of the seals means it's leaking. Similarly, after changing seals, it allows checking your work. Don't assume it's the propeller shaft seal that's leaking. It could be a failed driveshaft or shift rod seal located on the top of the lower unit.
When changing lower-unit oil, examine the spent oil for signs of overheating. Dip you finger in the oil, smear it across a finger. Sniff it. The telltale clue of burned oil is an unmistakable, burned smell and very black oil. Milky brown means water mixed in with the oil by the whirling gears. Broken chunks of gear teeth or bronze bits also mean serious mechanical damage. Dunk a magnet in the oil to discover metal bits you can't see with the naked eye.
When buttoning up, make sure each gear case drain plug wears one and only one gasket. Old gaskets are infamous for hiding inside the housing, and the do-it-yourself mistakenly believes the gaskets is lost. Two gaskets don't seal. Neither will none. To refill use a hand pump and quart bottle of lubricant instead of oil in a squeeze tube. Also, keep an oil absorbent rag handy to dab up errant droplets. Fill from the bottom plug until oil just begins to trickle out the top plug. Replace the top drain plug. Its vacuum seal will hold the oil in place long enough to insert the bottom drain plug.