The Cable Club in Red and Blue is very simple. Using a link cable you can connect with friends and play together. In these games there are two options; colosseum and trade, which we'll go into detail with below.

Trade Center
Trading with friends is an integral part of Pokemon. Though there are several in game trades with non player characters, it's often much more fun (and necessary to complete your Pokedex) to trade with a friend. Traded Pokemon grow at 1.5 times the speed of regular Pokemon. But beware! Outsider Pokemon over certain levels won't obey you unless you have the proper badge. The list is as follows:

Outsider Pokemon will loaf around, hit themselves, or fall asleep sometimes if you try to use them in battle and don't have the proper badge.

Colosseum
You can battle your friends with your in game teams as well. When playing against a friend, your Pokemon do not gain experience points and are fully healed after each battle. Make sure you heal before going in, however, as the Cable Club will not heal a party until after a battle is complete. You cannot use items in Cable Club battles and battle style automatically becomes "set", so be prepared. Running causes you to forfeit the game.