The most traditional way to wear a wedding and engagement ring set is to wear both rings on the third finger of the left hand. It is left to personal preference whether the engagement ring or the wedding ring goes on the finger first.
The tradition of wearing the wedding band on the third finger began with the once-held belief that the vein in this finger led directly to the heart. Customarily, the wedding band is worn closest to the heart. Others wear the rings in the order they were received: engagement ring first, followed by the wedding band.
Other factors may determine the order the rings are worn; for example, the tighter fitting ring may go on the outside to protect a looser fitting ring. The order in which the rings are worn, as well as which finger serves as the traditional wedding ring finger, can vary between cultural and religious customs.