while I don't have as much experience with outboards as many of the other guys here ( I would suggest that just like with a used lawnmower or anything other gas engine, you might do well to also consider as many engine basics as possible.
((Caveat: Honestly, I typically just hook up the battery and gas line and try it out hoping for some sort of miracle, but that's never happened for me on a motor sitting for more than a couple years... Sooo, This is "How I" approach it... (these are my thoughts and opinions and may not be the best advice for everyone or every motor situation) feel free to use them at your own risk and/or modify them to suit your needs.))
Here goes:
you know you need spark, fuel and air to make it run - so make sure you have those things (a clean carb is needed to run but not necessarily the first thing I'd do if trying to assess an old sitting motor) - you can run on some 2 cycle starting fluid to test the ignition etc for 20-30 seconds to make sure it's worth further time,money, and effort...
I like to test for spark first. I don't like to mess with ignition problems if I can avoid it so if it doesn't spark I'll usually pass on it.
Then test for fuel - you should get some fuel pressure out of the pump just running the starter. (have someone help you catch it in a clear jar from the line into the carb. look for trash etc before it goes in there. you might also find old watery sludge in there that never got drained or formed from condensation while sitting - or find cracked hoses etc.
Air - this is where the compression test comes in. If there is no air going in I think it will cause the compression to be lower (could be wrong on that) but being that a 2 cycle is a sealed unit I assume this to be true (you'll eventually also need to make sure you don't have any air leaks, like at the carb gasket or other places (you should be able to get it to fire up though just won't run as well or may not idle steady if extra air is getting in there). A compression test will tell you if the head gasket is blown out, rings are too worn etc. (some further diagnosis may be needed that is beyond the scope of here for knowing what low compression means)
So, in addition to the advice in the others' posts above here are the questions I'd ask:
-- what condition are the plugs in? they don't have to be new, but might need to be cleaned off and run a light file/sand paper or something on them to clean off the points (check gap also) - I assume if you get it running you'll get new plugs as a first step before going on the water anyway.
-- check the spark getting to the plugs (they have lots of contraptions to do this at auto parts store from those that light up and go inline with the plug to those that you clip to ground and screw out /in to get a gap distance. No spark at 3/8 to 1/2 inch or so would mean it won't run no matter how much you do with fuel and carbs.
--NOTE:*** !!! DON"T put fuel in cylinder head before checking this spark with the plugs out - you don't want to damage yourself or your motor etc!!!
-- I would probably shoot a little bit of oil or fogging spray or something into the cylinders and turn over a few times by hand then with starter so you know you have some lube in it before running the starter hard hoping oil/gas mix gets through the carb (unless you have already cleaned or rebuilt that). Not a lot but some. Oils in the cyl head may also change compression readings so you may want to check that before and after - extra oil on the rings can give you an artificially high reading even if the rings aren't in great shape.
-- is the fuel line from into the pump and carb rotten (I bought a 94 outboard last year that wouldn't run for anything even after the carb was rebuilt - fuel line to the pump where the tank hose connected was full of debris from the inside part of the line (outside actually looked pretty good).
-- is the fuel pump working?
-- are the carb jets clean? float working? is there a manual/auto choke - is that working?
-- run it in a barrel ( I was able to verify my water pump impeller was going strong by just running it on the starter and watching the discharge tube) No water = maybe you need to check/change the impeller sooner than later (make sure line is clear out from motor also) bugs like to get up in the tube and die.
-- You can check the gear oil for color before running it by letting off the drain screw with the top on still in. If black maybe that can wait till you get it running (here is where my limited experience shows - maybe you should just drain it and put in new gear oil from the get go - will refer you to others on that part - I do it one way on my motor but that's my money and problem - your milage may vary... )
-- I'm sure I'm forgetting something... so maybe someone else can help fill in any blanks.
