Be aware that transmission repairs are very expensive. Check it thoroughly.
Put up the hood of the car and check the transmission fluid with the dipstick.
Touch the dipstick and smell the transmission fluid on your finger. The fluid should be clean with no grit and it should not smell scorched or burned. If the fluid is dirty and internal transmission problem is evident.
Drive the car. If the transmission slips or has delayed the reaction, a problem is indicated. Try all gears, including reverse, park and neutral. Shift the car into neutral; the transmission should not engage at this time. Then, shift immediately into drive. There should be no delay. The transmission should engage immediately; the car should not jerk but should move ahead without hesitation. If the transmission does jerk or a significant delay (more than one second) is evident, run the other way as fast as you can.
Manual Transmission or Standard
If the car has a manual transmission, be sure to drive the car in every gear. They should all shift smoothly. There shouldn’t be any thunks, clunks, vibrations, jerks or weird noises.
When you are in second and third gears, accelerate quickly. When you do this, the clutch shouldn’t slip and if it does, it’s an indication that the clutch will have to be replaced very soon.
While driving, de-accelerate and accelerate to see how the car and the transmission respond. If you hear humming or whining, leave the car where it is. It will only cause you a very big headache. All gears should shift without noise or grinding.