Your specific description makes it sound like you already know what symptoms to look for.
A couple of things that can be done relatively easy:
1) Check for red puddles under transmission. If leak does not seem to be coming from either the drain plug (retighten) or the transmission pan gasket, expect the worst! Fluid may be leaking from the upper half of the transmission indicating worn parts. Use your best judgement when deciding to continue with the remaining steps, as your transmission may be beyond simple maintenance.
2) Check AT dipstick and make sure AT fluid is pink. If it's brownish and/or smells burnt, you are looking at internal transmission damage. Verify that there is no smoke coming out of the dipstick when you open it. If fluid is burnt, a fluid replacement may be too late and will simply result in another batch of burnt fluid after minimal transmission usage afterwards. If it's still pink, compare the level of lubrication that it still provides versus new AT fluid. Use your best judgement and/or knowledge of the car's transmission maintenance history.
3) If fluid is pink in color, make sure it's at the proper fluid level. To do so, drive the car for ~20 minutes, then let it idle for at least 2 minutes on your driveway (level surface). Check dipstick for fluid level. If it is above the limit, drain fluid! If you go over the capacity, you run the risk of aerating the AT fluid while the transmission is under stress. Making sure that the AT fluid level is not above the limit is almost more important than making sure that it's not too much below the limit. Note: AT fluid needs to be checked when its hot, since heat makes it expand.
4) Buy a fuel/vacuum gauge and check vacuum at the AT transmission modulator (driver's side; ~center of AT). 10-20 inches of vacuum are desirable - use your best judgement with older transmissions that may require more vacuum (within the mentioned range) at the modulator. If this is not the case, check car's vacuum system for leaks, replace worn rubber intersections and torn/brittle vacuum lines. Do so by systematically tracing vacuum lines from the master brake cylinder to major vacuum intersections and temporarily plugging them. If you have 10-20" of vacuum, make sure that it subsides proportionally with the throttle (i.e. half throttle = 1/2 vacuum, full throttle = no vacuum). 1 meter of vacuum hose is $1. Rubber intersections can be bought for ~3 each.
5) Replace transmission filter & buy a new transmission pan gasket for reassembly. If the oil flow in your transmission is restricted, it may explain the problems you are experiencing. Use a Dexron III fluid to refill.
Extra step (once fluid has been added after filter replacement -- may reuse drained fluid for this step, if no outside particles and/or dirt were present in the container used to catch the AT fluid in the first place): Completely purge existing AT fluid from the torque converter by disconnecting the AT oil line leading to the radiator on the driver's side. Have an assistant ready to cycle through P-N-R-D-3-2 positions while you fill in new AT fluid through the dipstick. You should end up with 7-8 quarts of AT fluid in the receptable, catching the AT fluid as it is being pumped out of the transmission.
The steps should be followed in sequence, since monetary costs involved will go up with each step. If none of the above help to improve your transmission, then you are looking at a transmission rebuild or swap. Removal of the transmission takes around 5-6 hours and will require a substantial lift (6 ton jack stands -- 24" lift).
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