I just went through this with a 1991 Honda BF45 and I had to buy compression tester, leak down tester and carb sync tool.
You should google "outboard compression test" and "outboard carb sync"
Compression Test (must be done at operating temperature):
This measures the amount of compression your pistons generate when they go up on the compression stroke.. If you get low compression in any cylinder will indicate leaky intake or exhaust valves, piston blow by (rings) or cracked engine block.. They key is to look for highly variable between results.. for example if your cylinder one and two is close to each other, but cylinder 3 is way off, then you might have a problem.. First you screw all your plugs OUT, then this kit, which is simply a pressure gauge with a spark plug treaded hose, screw into the spark plug hole and then you crank the engine for about 5 seconds.. (You repeat the test per cylinder).. AFAIK your BF50 new should do around 210psi.. but anything 180 and up is probably good, depending on the age of your motor.. the key is to see how close the cylinders are relative to each other..
You can rent these kits or buy inexpensive ones.. I bought a super nice set called "OTC 5605 Deluxe Compression Tester Kit" from Amazon for $80
Leak down test (at operating temperature):
If you see problems on the above compression tests, you have to do a leakdown test, this will indicate where the leak its and why your compression is low for that specific cylinder.. You need to manually put the cylinder in top down center of compression stroke, this means all valves are closed and piston is in its highest position, then screw the kit into the spark plug hole and supply about 90-100psi of shop compressed air into the kit.. the leak down test kit I have, has 2 gauges and shows the regulated supply air pressure, and will show what pressure is being kept in the cylinder.. it basically has a super small orifice that will bleed gas into your cylinder and if your cylinder has a leak, it will leak gas faster than what comes in, so your cylinder wont keep the air pressure the same as the input air.. So, if you show a big difference in input air pressure and the pressure of what your cylinder can hold,it means you have a gas leak somewhere and the bigger that difference, the worse the issue.. Then you need to listen where the gas is hissing.. for example put your ear on the intakes to hear if the intake valves are leaky, you depending on how well pronounced the hissing is, you can tell if its piston, valves or cracked head..
You can rent these kits or buy inexpensive ones.. I bought a really nice "OTC 5609 Cylinder Leakage Tester Kit" from Amazon for $70
Vacuum Gauges (For carb and fuel injection sync):
Finally the vacuum gauges or "manometers" will tell you how much vacuum for example your carburator or fuel injection intake creates.. And you can hook up one per cylinder and compare how much air each cylinder draws in.. You really want to syncronize them all so they have as close as possible the same air intake.. For example, I have carbs on my Honda BF45 and you need to syncronize them well to have good running and idling motor. Essentially you hookup a gauge per cylinder, run the engine and then adjust idle speed, then sync all carbs to the "master" carb so they all have the same intake vacuum..
Usually if you have really rough idle and issues with throttling up to speed, a good carb sync will do the trick.. Provided your carbs are not gummed up to begin with and needs a rebuild..
You can rent these or buy inexpensive ones, they are not all the same, I did a LOT of research and eventually settled on a carb sync tool from europe that doesnt use fluids or mercury, it uses stainless rods.. its a bit pricey, but well worth the money..
I bought the "Morgan Carbtune Pro 4" from Amazon for $120
Hope that helps