You might be somewhat limited when it comes to diagnosing automatic transmission problems. In addition to the special tools you need to repair them properly, there are also special tools for diagnosis. One of the main tools is an automatic transmission pressure gauge.
This is one of the main diagnostic tools for automatic transmission problems. If you do have one of these tools, great. You'll also need the service manual, which can tell you where to check the pressures as well as what those pressures should be. There are several pressure ports on the transmission. Knowing which ones to check and what pressure you're supposed to see is a big part of automatic transmission diagnosis. If you don't have access to an automatic transmission pressure gauge set, or the service manual information, here are a few general tips to get you started.
The first thing is to be able to differentiate between an automatic transmission problem and an engine performance problem. Much of this is covered in the Engine Performance Article, but I'll go over it again here briefly. One of the easiest ways to find out if it's an engine performance issue or an automatic transmission problem is to do a power braking test. In this test, you put the vehicle in drive or reverse, set the parking brake, hold your foot on the vehicle brake, and floor the gas pedal. The RPMs should top out somewhere in the 1500 to 3500 RPM range and hold there. If it's an engine performance problem, it will likely show up here, as you are putting the engine under an extreme load. You don't want to do the test for too long for that very reason, as you could overheat the engine. You're just performing a check here, you're not trying to blow up your engine.
Another test you can try if you're having a shifting problem is to shift the transmission manually if possible. Some automatics have the ability to move the shift lever through the gears manually one at a time. Some only allow you to shift from second, but that's better than nothing. The point of this test is to see if the transmission acts normally when you shift it yourself. If it does, this might indicate a problem with some of the automatic transmission controls and not the actual gears themselves.
This might or might not work on transmissions that have the upshift/downshift or sport mode feature. With these transmissions, you can take manual control of how the transmission shifts; they’re mostly referred to as sport shift or something like that. This is basically a manual override, but it still uses the same electronics to shift the transmission as it uses in automatic mode. What I'm talking about is physically moving the shifter from gear to gear, not just using paddle shifters or a special mode for the shift lever. You might get results shifting with sport shift, but as I stated, these modes use the same electronics to shift the transmission as the automatic mode does and you're not moving the manual valve in the transmission that mechanically selects a gear. Because of this, you won't get the same result.