Clean the book.
If the cover is uncoated paper, you may be able to use an eraser to remove some smudges, but be gentle.
If the dust jacket or paper cover is glossy, you can take off dirt and stray marks by spraying a little Windex on a paper towel and gently wiping off the cover. Be careful not to get Windex on the pages. Sometimes a slightly damp dishcloth is all you need. Give the book cover a moment to dry out before you wrap it.
Lighter fluid can be used to remove stubborn stickers from glossy covers -- soak the sticker for 20 seconds or so and then peel it off -- but keep in mind that lighter fluid is harmful to skin.
Protect it from moisture. When the cover has dried, wrap the book(s) in some kind of plastic in case the box gets stuck under a drain spout at some point along the way. The plastic sleeves in which newspapers are delivered to homes are the right size for most books. Put the book in the bag, fold over the top of the bag, and tape it with packaging tape. Don't over-tape; use just enough to tape down the edges. It's a pain if the recipient has to cut off yards of tape to get to the book.
Add whatever notes you want the recipient to get.
To qualify for the Media Mail rate, which is the best shipping rate the U.S. Post Office offers for books, don't add personal letters or non-book items, or you'll have to pay the higher Parcel Post or Priority rates. Mail a card by itself and tell the person that a book is coming separately. (The card almost always arrives first.)
If you didn't include a commercial packing slip, write a duplicate address label to include inside the box in case the original label is torn off or becomes otherwise unreadable.
Consider sending a paperback book in a padded envelope. A box is still best, especially if the book is valuable or sentimental to either you or the recipient. However, paperbacks don't have the overhanging covers and exposed corners that hardbacks do, so they travel better in envelopes than do hardcovers.
Use a box that is larger than the book. For hardcovers, find a cardboard box that is a little larger than the book. If you don't mind paying the higher Priority Mail rate, you can use the Priority Mail boxes that the post office provides free (it's a service you get for paying more). But you cannot use these boxes and still get the cheaper Media Mail rate.
Make a reused box look fresh. If you're reusing a box, you can make it look nice for the recipient by turning it inside out. Just find the spot where the box is glued together. Usually it's just one seam. You can separate that seam with a butter knife, turn the box inside out, and retape that seam. Voilà! You have a nice, clean box. If you reuse a box but don't (or can't) turn it inside out, scribble through the old addresses, labels, and markings with a big marker, or put adhesive stickers over them.
Tape the bottom. You know how you can fold the flaps of a box together so you don't have to use tape? Don't do this when you're shipping books. Fold the small side flaps in, then close the large flaps so they meet perfectly and tape the seam with packing tape or strapping tape. Leave plenty of overhang for the tape to go up the sides of the box, which makes it stronger.
Add packing material. Set the box right-side up, with the top open. Layer the inside bottom of the box with some packaging material -- packing peanuts, air bags, Styrofoam, crumpled plastic grocery bags, or crushed newspaper as a last resort (newspaper is relatively heavy and adds to the shipping cost).
Fill in the box. Set the book (wrapped in plastic) on the layer of packing material. Fill in the space around the book with more packing material, then fill the box to the top. You want the book to stay firmly in the middle of the box and not slide around.
Can the book still shift? The key is to close the flaps of the box when you finish packing, but don't seal it yet. Shake the box. If you can feel or hear rustling or movement, add more packing material until the box is packed just enough to prevent any movement within. This will protect the book from getting beaten up, no matter what your box goes through.
Write the address on the top flap of the box before you tape it closed, or put on an address label. Look up the 9-digit zip code under 'Find a ZIP Code' on the US Postal Service website; this will speed your package along its way. Write in ballpoint pen so the address won't smear if it gets wet, then cover the address (or label) with clear packing tape.
Tape the box closed. Tape the top seam with one long piece of tape, then put tape over all the side seams as well to strengthen the box.
Take the package to the post office. If you want to see how smart you are, ask the clerk the difference between Media Mail and Priority Mail rates. Wow! If you qualify for Media Mail rates, you saved a lot of money!