Here is what you will need:

Leather – If you have scrap, an old jacket or wallet, anything soft and malleable, have it ready! Scraps of many colors are also available from many sellers on Etsy.
Fabric – This will replace mull (a starched cheesecloth) that will be glued directly to your book block to strengthen your book.
Thread – For the headband. Aim for something thick that will take up space. You can also use a pre-made headband.
Scissors – For trimming your cover. If you are using leather for your cover, make sure they are sharp!
Hammer – For shaping your book block. Be sure it is clean as it will be coming in contact with your paper! (I used a rock hammer and my pages don't hide it!)
Glue – For gluing your leather to the front and back covers of your book. Elmers works!
Heavy Book – This will be your book press! Any heavy book will do, though I find art books (and their dense pages) perfect for the job!