Last year I wrote a fairly popular guide on leather-binding paperbacks. Since then I've done some more experimenting and come up with a method that I think is a bit easier and turns out nicer.
The Gist: Carefully peel the existing paper cover off of your book.
The Gist: Rub off the fuzzies.
Detail: Rub them off. Use your thumb, or an eraser, or maybe a little bit of sponged-on water to soften them. Don't get too crazy, just clean it up a little.
The Gist: Get two pieces of paper you'd like to see inside the front and back cover of your book.
Unnecessary Trivia: If you want to sound smart, you can call these pieces of paper "endpapers", "end-papers", or "end-sheets". The side glued to the cover is (creatively) called the "paste-down". The other part is called the "flyleaf".
Gist: Fold each piece of paper in half. Crease goes with the grain.
Why "with the grain"?
The Gist: Trim to match the size of your book.
Detail: If your book is 6 inches wide and 9 inches tall, trim the folded paper to 6 inches wide and 9 inches tall.
The Gist: Glue the folded paper onto your book. Glue should only extend about 1/4-inch from the spine of the book.
Glue: Elmer's glue ($3) is probably fine. There's also special bookbinding PVA ($8) that's essentially the same thing, but marketed for book binding. Weigh your risk-averseness / perfectionism against your cheapness / laziness.
The Gist: Glue a piece of fabric onto the spine.
Unnecessary Details: This piece of cloth is called a "super". It adds a little bit of strength to the spine and helps keep the papers from peeling away from the book when you put your covers on. The old-school way was to make it out of cheese cloth, but some people say cheese cloth is too weak. Making it out of muslin works well, or you can even buy yourself some special cloth marketed specifically for making supers out of. The important thing is for the cloth not to be too thick (like not felt or velvet) and to be fairly stiff (not too stretchy; don't use your mom's old nylons). I use old pillowcases/sheets.
The Gist: Glue some cool-looking folded cloth at the ends of the spine.
Unnecessary Trivia: Headbands used to have a structural purpose. In most modern books, they don't. But they sure look cool.
The Gist: Get some cardboard to make your covers out of.
Detail: You want something sturdy, about 1/16 inch thick. I used chipboard from Amazon for this project, but I've used the back of sketch pads before too. I wouldn't recommend corrugated cardboard (like you'd get from a box), because it seems like it would crease and dent too easily, but I've never actually tried it... maybe it's awesome!
You'll need enough for 2-4 pieces that are just a hair bigger than your book.
The Gist: Cut the cardboard about 1/4-inch taller and 1/4-inch narrower than your book. Grain should run from top to bottom (just like the papers).
The Gist: Use extra cardboard to glue a second partial-layer on each cover piece.
Details: The sky's the limit. You could even X-ACTO the edges of the second layer to get rounded curves and stuff. Just realize that any gaps that are really small (like less than 1/8-inch) will be hard to get the leather to conform to.
The Gist: Cut a piece of paper or card stock to give a little shape to the spine of your new leather cover.
Detail:(see the red piece in the diagram)
The Gist: Lay out your covers and spine and tape them to keep them that way.
The Gist: Pick out some leather (or other cloth).
Where to get leather: If you live close to a leather store like Tandy Leather, go in and see if they have anything for sale (I found a nice big sheet of this black-dyed pigskin for like $20). Otherwise, check Ebay or Tandy Leather's online catalog, or get a free leather couch on craigslist and cannibalize it. I would stay away from vegetable-tanned leather (unless you're planning to finish it yourself). Anything you find on furniture or upholstery is probably fine, as long as it's flexible and you like it.
The Gist: Glue the leather / fabric onto the covers. Press it into all the nooks and crannies of your 3D cardboard design.
The Gist: Leave a margin of about 1-inch on all sides. Trim the corners at a 45° angle, leaving an overhang about as big as the cover is thick.
Detail: Use scissors, or an X-ACTO knife, or an axe (if you're Paul Bunyan).
Fold and glue the top and bottom.Keep things nice and tight. Set a weight on top for a few minutes to make sure the glue has set.
Pay special attention to the corners of the two folded slides. Add some extra glue and crease with a table knife or something if you have to.
Keep things tight. Pay close attention to the corners and make sure they're pressed down well.
Lay your book on one half of the cover. Make sure the cover overhangs by about 1/8-inch. Fold the cover over the book and make sure everything fits nicely.
If you left the ends of the fabric on the spine dangling in step 7, glue them down to the papers now. Pull them nice and tight.
The Gist: Glue on the front and back covers, but not the spine or the gap next to the spine.
The Gist: Stack some books or weights on top of your book for a good day or two while everything dries.