How do you check the transmission liquid on a 65 mustang?

Automatic: there's a dipstick on the passenger side of the engine close to the firewall. Check it with the engine warmed up and the transmission in 'Park' or "P"

Manual: The car will have to be jacked up and level, then there are two plugs on the side of the transmission case. Loosen the upper most plug, and if liquid runs out, it's good. If liquid doesn't run out but is inside about 1/8 1/4 of an inch below the opening, it's good. If it doesn't run out and is lower than 1/4 inch below the opening, then fill with 80w90 gear oil.

Good luck.

If it's an auto, attempt the dipstick that says "transmission fluid"
If it's a stick shift manual transmission as I suspect, you do not.

If its an auto you may want to look for the dipstick near the
rear of the engine. But you most likely mean a manual
transmission. Then you must get underneath and find the
filler pipe plug on the side of the transmission. Remove
it and you may have to put your finger in, the liquid should
be near the bottom of the hole.

Go with Doug K recommendation.

check the transmission level after the car was driven and warm, with the engine running and the car in the park position on level ground check the liquid level on the transmission dipstick.