I went thru this, there are pretty much two types, the older ones operate on a different frequency, and use dip switches to set the code, very simple to use. Newer ones use a different radio frequency and usually a rotating code.
You most probably need the earlier type, just open up the receiver up on the opener head (the receiver may be a small box mounted off to the side of head unit, with a wire dangling down - that's the antenna) and see how the little white 2 position toggle switches are set, then set the remote the same way - it should then work. Buy one of those from C&C, put a new battery in it, set the switches and off you go...
We had a garage door opener in the early 50's, even then they used remote transmitters and receivers.
One of those grey ones in the top row in C&C's pic will probably be the right one, he can open it up and see how many switches are in it, you want the same number - usually 5, IIRC