In Minecraft, I created a church and made a solid golden altar. I typed up The Book of Matthew in a book and quill and then signed it. Can I place this on the alter so it can be read? Can I even place a book at all? Is there a mod that would allow me to do this?
There is no vanilla way to place books in the world (except in a chest as MBraedley says).
Bibliocraft however has various ways of storing books in the world, the best looking way for a single book would probably be something like the desk:
The desk will keep one book open (it can store up to 9 at a time in the latest version of Bibiliocraft) and right clicking on that book (if it is a book and quill or a written book) will allow you to read from the book directly. It will also store the page you were reading from when you exit the book.
You can place an item frame, then place the book inside it. This will allow players to come up and see the book in the frame, then click it to take it into their inventory and read it.
Note that as of the latest snapshots, clicking an item frame once will give the item, and clicking an empty item frame will remove it from the wall. This lets you keep the item frame in place when the book is removed.
You can WITHOUT mods or hacks place the book in an item frame or a chest or one of the different kinds of chests.
I understand that this is an old question but here is how I would do it in vanilla minecraft. Make an enchantment table and place it somewhere where the altar would be, then make a chest nearby and place the book in it. Although this wouldn't let you read the book from the enchantment table but it will seem as though the book is there since the texture is practically the same. The enchantment table will also add a little cool thing where whenever you go near it the book will open and flip through. So if you think of it, it would look as though you are reading the book from the table but in reality it is in your hands.
It will work if you place a book and quill on a lectern (which looks like a pulpit if you ask me).
there is no legit way in minecraft vanilla (as of 1.6.2) to read a book without holding it
although as said above you can get a mod for that (best place to get forge mods is http://www.skydaz.com/)