First: contact a trader within your friends or in marketplace forums, setup a deal defining cars and trade conditions. Every PS3 (not account) have one car trade slot every day, so use it carefully. Experienced traders have larger car "catalogues" but a very long trade schedule. Beware of scammers.
Second: exchange Friendship Requests. It must be done from XMB.
Third: new members are usually asked to send their car first. To do
1) go to the garage
2) select the car WITHOUT starting the engine: it adds a switch to the car and may invalidate most of the trades
3) select "send to a friend", and confirm
Fourth: wait the other party for sending its car
Fifth: enjoy.
