This instructable covers the steps for a very cheap and in my case a rather crude Kindle Fire cover. Some of my pictures didn't turn out well "but" by looking at the results I hope you can easily see what I did. If not, ask questions.

Step 1: Gather Materials & Tools

Materials

A book of questionable value equal to or larger than 9-1/2" X 6" X 7/8" thick. The dimensions of the book are so you will have ~ 1/2" clearance around your Kindle inside the cover. I paid $1.00 for mine at a thrift store. -OR- something nice like a Moleskin notebook with a strap to hold it closed. Your choice.
Three sheets of dense foam from a craft store. I got mine from Michaels @ $.99 each. If you want to be really frugal you can get by with one.
Two thin hair bands. I took two from a card full I bought for a $1.00 I have in my car for my girlfriend who never seems to have one when she wants to put her hair up. You might have a couple just lying around or someone willing to donate to the project.
A strip of duct or similar tape.
White glue.
Some cardboard about the size of the Kindle for a template.
If you want a strap, about 4" of Velcro strap.

Tools

A carton cutter or similar.
Something to measure with and if necessary you can just wing it using your Kindel to get your cuts close enough.
Straight edge.

Of course use caution with the blade. Any blade can injure and stitches or worse aren't fun. Don't bother asking how I know.

Step 2: Remove the Book Pages

Leaving the heavy paper flyleaf, carefully remove the pages.

Step 3: Cut the Foam

You will need to cut three (3) pieces of foam:
The outside dimension will have to match the inside size of the book you purchased.
The Kindle Fire is 7.5×4.7×0.45 inch (190×120×11 mm).
The INSIDE deminsion length and width of two of the pieces has to be ~ 1/8" larger than the Kindle so the Kindle will fit inside the foam with ~ 1/16" clearance. I used 7-5/8" X 4-3/4" as close enough.

I suggest you cut out a couple of cardboard templates and stack them to more or less equal to the Kindle's ~ 1/2" thickness as it will be useful later. By using your Kindle as a template, you can draw around it, cut out the cardboard, and use the cardbord template rather then a measuring device.

Cut out three pieces to the outside dimension necessary to match the size of the book you purchased to make a bottom, center, and top piece. You can use the pages as a cutting template for the outside edge of your foam.
Set the bottom piece aside.
Use your cardboard template and cut out the center of the other two pieces.
Set one piece aside as the top piece.
The last piece will be cut like a "U" with the length staying the same. In other words cut parallel to the length so the arms stay long.

If you mess up, don't worry, glue can fix a lot. I ended up gluing on strips so if you want to be frugral, you could do that too.

Step 4: Glue It Up

Stack the foam with the "U" piece in the center and glue them together. I used white glue and it worked just fine. Your stack will look like the introduction picture. Rather than using your Kindle, use the stacked cardboard to keep the pieces from sliding around while the glue dries. I used some books as weights but learned it can cause the foam to slide around so check your stack.

Let the glue dry at least an hour.

If you find the pieces slid around into the space where the Kindle sits, just trim them with your cutter.

The open "U" will be at the bottom of your cover. This is so you can reach the on/off button and the USB port.

If you want to cover the raw edges/reinforce the binding, open the book cover flat and lay a strip of duct tape or similar down the middle of the book back. I used red 'cause I had some.

Take the two hair bands and wrap them around the whole stack. Place them so the top one is at the bottom of the black edge, and the bottom one is about in the middle of the black edge. See the picture in the introduction.

If you want you can use some Velcro and make a strap to hold the cover closed. Glue your stack on top of a strip of Velcro with the strip sticking out perpendicular to the book edge. I'd use the loop part for the strap. Glue a square of hook to the inside of the left cover.

Or you can glue a square of loop to the foam edge and a square of hook to the inside of the left cover. Or you can spend a bit more and cut apart a book that already has a strap.

Glue the stack inside your book and let it dry for as long as the manufacturer specifies. Insert your Kindle and your done.