Contact a used bookstore. Before you throw away your books-or even pack them up (see step 3 below)-see if a used bookstore is interested in buying your collection. You can describe what you have over the phone or ask a store representative to stop by for a look. Be aware, though, that books depreciate tremendously in value, so it's unlikely that any of your volumes are worth more than $1 or $2 apiece (and most will probably earn you less than 50 cents).
If the used bookstore isn't interested, contact a thrift store. Unless you collect rare Shakespearean folios, odds are you'll find that the total value of your books isn't worth the hassle of negotiating with a used bookstore. In that case, consider donating your books to a thrift store or the Salvation Army. It's possible that you can arrange for the store to pick your books up, but most likely you'll have to bring them over yourself.
Pack your books in sturdy boxes. Books have straight edges, meaning the most efficient way to pack them is in rectangular cardboard boxes-not jumbled together in an endless series of shopping bags. If you're going to be moving these boxes yourself, be careful not to pack too many books in each (unless you want to be reading the eHow about "How to Recover From a Sprained Back").
Give folks an opportunity to snag some favorites. It's a shame to throw out perfectly good books, which is why you should place your boxes out on the sidewalk on a sunny day, along with a sign saying "Free Books!" By the end of the day, passersby will have picked out the volumes of interest and you can throw out the remaining books the way you normally would-either by leaving them with your household trash or driving them to the dump yourself.