Cover the flooring underneath the wall. Drywall mud is difficult to get off flooring. Lay down plastic dropcloths underneath your work area. Put on gloves to keep your hands clean.
Clean debris out of the crack. Use a chisel and your hands to break free any hanging debris around the crack.
Fill the crack with expanding sealant foam if it is a large crack. Shake the can, hold it upside down and fill in the crack between the walls. Do not overfill -- it will expand. Wait until the foam hardens or sets, usually between 45 minutes and two hours.
Scrape off excess foam. Use a utility knife to cut away foam that has extended beyond the edge of the crack.
Cover the crack with drywall tape. Self-adhesive drywall tape works best. Tape over the entire area.
Apply joint compound over the tape. Use a putty knife or a drywall knife and apply a thin layer of joint compound or drywall mud over all of the tape. Scrape off excess as you go. Let this set.
Sand the area smooth. It's nearly impossible to apply a smooth coat of mud. Use a medium-grade sandpaper and sand over your joint compound until the area is level and smooth to the touch.