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Purchase a set of Velcro straps. Use a stepladder and a pencil to draw a horizontal line where your bookcase meets the wall. Remove the books and move the bookcase away from the wall. Mark the stud locations with a pencil. Ask someone to line up the straps vertically and hold them in place. Drill the wood screws into the center of the straps, where there are holes for the screws. Move your bookcase back into place, at the level where your screws are placed in the wall.
They should include long screws and wall anchors that will hold the straps firmly to your wall. You will not need to drill into the case itself using this method. Use a stud finder to search for wall studs. If possible, find two studs and secure the bookcase with two straps to ensure a good hold. Secure the bookcase into wall studs whenever possible, instead of using wall anchors. It is best to secure the bookcase without the books in it, and then fill it up once you are finished. Draw a vertical line. The two cross-hairs are the locations where you will drill your wood screws into the wall. Make sure the adhesive layer is facing down. You will peel back the clear plastic cover after you are done drilling. Use a cordless drill. The number of screws may depend on the brand of Velcro straps you use. If you couldn't find a stud, you will need to make pilot holes and insert the wall anchors. Then, screw the wood screws directly into the wall anchors, where your lines meet. Peel back the clear cover from the sticky adhesive and press the strap onto the top of the bookcase. For best results, don't remove the adhesive strip to realign, or it may lose some of its hold.