Our dog Dodger will rip apart normal dog toys in about 15 minutes. "Indestructable toys" take a little longer ;)

I learned how to make a monkey fist knot at a juggling festival a few years ago -- just for fun I made Dodger a toy out of rope that managed to keep him busy for at least a few days...

Step 1: Materials

Rope: At least 10.5 feet of 3/8" diamond braid rope -- about 4.5' for the monkey fist knot and 3 feet (X2) for the braid on each end. It's better to start with a much longer piece of rope, tie/position the monkey fist knot, and then trim off the long side. Also, forming the monkey first takes more rope (~6'), which is then tightened down to 4.5'.

Scissors or a sharp knife to cut the rope (Be carefull!)

Lighter to melt the rope ends, to prevent fraying.

Step 2: Monkey First Knot

A monkey fist knot is basically three (or more) turns of rope, three more turns around the first three, and a final set of three more turns locking them all together.

Two good sites (with pictures) of how to make a monkey first knot are:
http://animatedknots.com/monkeysfist/ and
http://www.igkt.net/beginners/monkeys-fist.php

Start about 10 feet from the end of the rope -- this'll give you about 6' for forming the knot + 3' for the end braid + 1' for tightening...

The initial knot has to be pretty loose, otherwise you'll never be able to feed the last three loops through the knot.

To tighten the knot, start with the rope at one end of the knot. Almost as if you were trying to untie the knot, push/pull the rope into the knot, creating a loop. Following the path of the rope, push/pull the loop through the entire knot, pulling the loops tighter as you go.

Cut/trim the rope as needed to end up with a monkey-fist knot in the middle of two 3' ends of rope.

Step 3: Cleaning Up the Rope Ends

I like to remove some of the rope core before fusing the ends of the rope.
Pull the braided covering back from the end, exposing the core.
Cut off an inch or so of the core.
Pull the braided covering back over the end of the core.
Use the lighter to fuse the covering together.

Step 4: Braid Knot the Rope Ends

You could stop here, but making a braid knot out of each end of the rope makes a better/thicker handle for the toy. A braid knot is a way of braiding a single rope.
See http://www.layhands.com/Knots/Knots_Decorative.htm#Braid

Loop one end around twice to form the three strands you'll be braiding (see the picture).

Start braiding the three strands near the monkey first knot.
As you braid, the other end of the rope will become tangled -- after a few plaits, stop to untangle the ends, then continue braiding.