Automatic transmission- Check your transmission fluid on level ground while the car is in park running. If that about right look at the fluid and check for dirtyness or evidence of small metal particles. If this is the case DO NOT CHANGE YOUR FLUID OR TRANNY FILTER. I know that if you do this and your transmission is already shifting hard it wont be long until you lose your transmission.
Manuel Transmission- Make sure fluid levels are good. You wont have a dipstick to go by here. Most cars you have to actually climb under undo a bolt and make sure the fluid is up to that point. Check for papery metal shard. If present consider replacing your clutch and pressure plate. Most likely if you do this a new throw out berring will be in the kit. Replace that as well that could be a reason for hard shifting.
Manuel Transmission- Make sure fluid levels are good. You wont have a dipstick to go by here. Most cars you have to actually climb under undo a bolt and make sure the fluid is up to that point. Check for papery metal shard. If present consider replacing your clutch and pressure plate. Most likely if you do this a new throw out berring will be in the kit. Replace that as well that could be a reason for hard shifting.