Hitching out of anywhere on the East coast of Australia is pretty easy, and Brisbane is no different. Head out onto one of the highways/motorways/freeways. The Pacific Highway goes south to the Gold Coast, Byron Bay, Sydney, etc., and the Bruce Highway goes North to the Sunshine Coast, Townsville, Cairns etc.
The best spots are going to be on on-ramps. If going south the best spot is just off Stanley St in Woolloongabba. For North, head out towards the airport (through the Fortitude Valley) and follow signs to the airport. The on-ramp onto the motorway in Hamilton is a good spot, too.