Test all the basic functions of the tractor, PTO, steering, gears, lift, lights, indicators and hydraulics. Even if you wish to work on it immediately, you may not be interested in a complete refurbishment for some time and need to reduce the number of things to do when you get the tractor home. Your check list should included at a minimum the following: does it start easily from cold, run well when hot, all the electrical components work well, does it have good traction If possible you should go to your test armed with a toolbox containing a compression tester, expensive Fluke digital multimeter, hydrometer, and other specialty tools. or bring somebody with you who has these tools.. If you don't have these tools, don't panic as these tools can end up costing more than the tractor itself.. You should in this case rely on your own common sense and your own observation skills.
Does it start easily? - A tractor that starts easily may rule out several items at once Good Battery, compression, ignition wiring / magneto, tune up, fuel flow, Carburetor can be assured (not guaranteed) by this. If it doesn't start quickly from cold, it still may be a good machine but you will need to spend some money on it . One key thing to watch out for is if the tractor is out and warmed up prior to your arrival, you lose an important checklist item, namely the cold start, because as we all know a warm engine starts much more easily then a cold one..
How does it run when warm - Getting it hot is a must if you want to find out how it will work after you plowed the first row. When warmed up you should watch out for a number of problems. Plan on spending a half-hour running it. Look for leaks, antifreeze and both oil. Once warmed up, stop it restart it again..
How well do the brakes work - Although inexpensive to replace, they are inaccessible on many tractors and will require extensive teardown to get the new ones in.
Does it smoke - Blue smoke spells trouble like rings, pistons, or valve guides. Smoke that looks black or white can frequently be sorted out with carburetion or ignition changes but still means work.
Does it make clunking noises from inside the engine - A simple ticking from the top of the engine may be a simple valve readjustment but a deep thunk from the bottom or middle of the engine would point to very serious and expensive repairs. The clunk should be more pronounced under load. This may be an indication of problems with the piston, bearings or crankshaft rods. And mean a very expensive repair job.
Use the hydraulics - Check the full range of the rams by extending them with a load. Let the load stand in the hold situation for a period of time to be sure that there is no leakdown. Clacking noises from the pump while lifting suggest the pump is getting insufficient flow of hydraulic fluid. The pump might have experienced a lot of wear when run this way for long periods of time and may be ready to fail.
While some of the above examples may sound a bit negative, you should do your research make sure you are aware of the specific issues a tractor may have before you invest.