Empty the bookcase
Move the bookcase close to the wall
Locate wall studs with a stud finder
Mark stud positions on the wall
Mark matching anchor points on the bookcase top
Use anti-tip brackets or furniture straps
Drill pilot holes in the bookcase
Attach brackets or straps to the bookcase
Align the brackets or straps with the wall studs
Drill pilot holes into the studs
Secure the brackets or straps to the wall with screws
Tighten all fasteners firmly
Check that the bookcase does not wobble
Reload the bookcase with heavier items on lower shelves
Recheck the fasteners periodically