Stuff the batt into the wall or ceiling cavity. Whenever handling fiberglass wear proper safety gear, including respirator, enclosed safety glasses, gloves, and a long-sleeved shirt.
Cut batts to fit, rather than compressing them, which can reduce R-value. Use a sharp utility knife to trim the batt 1/4" wider and longer than the space. Use a stud as a straightedge and cutting surface, or measure and cut on the subfloor. Cut the unfaced side on faced batts.
Install polyethelene vapor barrier over unfaced batts by draping it across the entire wall, a few inches over on all sides, and stapling it to framing. Cut around obstructions and seal with vapor barrier tape.
Install faced batts by tucking along the edges so that the flange is flush with the edge of the studs. Staple flanges to the face of framing members, spacing staples every 8". Patch gaps or tears with vapor barrier tape.