How do I copy the programme from one electronic gate key fob to another to give me 2 fobs

You don't. You get additional ones from the dealer.

Without any model numbers, you probably train the receiver to accept the new Keyfob although the procedure used in my car to program a RFID key rivals wierdness. Lately though, key programming is becoming a dealer only OEM scan tool option.

Could be as simple as press this button on receiver. Press keyfob until x light blinks.

An alarm system I have uses voice prompts to erase and add transmitters with the "secret button". Linear (Linear Technology - Linear Home Page) makes a lot of RF stuff for alarm companies.

Don't today's key fobs have a revolving set of codes, i.e.. A challenge-response system?

They are not two way communications, but some do use a revolving code set known only to the manufacturer. So, for garage door openers, mom and pop can have different door keys.

Exactly how it works, who can guess. Say a transmitter spits out 3 codes and the door opens. Another xmitter spits out three codes and the door opens. As long as the sequence is known by both, your fine and it's not the same 3 each time. Hence, revolving codes. Or if the codes are continually transmitted in a specific order and when the opener gets a few in a row, it decides to open the door.

Homelink in cars allows one to learn a transmitter, so I suppose it's doing exactly that. Remembering the code sequence of the transmitters when the button is held down.

The transmitter could also have a unique serial number and use that as part of it's sequence.

There is a chip from one of the manufactures that creates a unique 128 bit number which can be read. Using this info, which make a lot of combinations, the key is learned. The car computer only has room for a few codes, say 8.

See: HomeLink; Home automation,Wireless control system, universal transceiver, RF control, Home security, smart home, vehicle to home, home automation, remote control lighting and home control