Determine which direction joists or rafters above the wall are running. Support walls have load bearing members above them perpendicular to the wall and are usually supported from below by foundation members or beams. It is an important question to resolve, and if you don't know, it is well worth having an expert look at your project and advise you. For minimal costs you can have someone come in and answer a lot of relevant quesitons. Think home inspector, contractor, construction consultant, architect or engineer.