I saw them for sale at Walmart you might be able to take one out of the box and get an idea as to how-to.

I had a look on line and those I saw were basically a tube of doubled fleece with openings at each end and were only for small dogs.

This is how I'd do it:

Cut the the outside fleece(B) double the width of the dog standing up and 1 1/2 times it's length

Then cut lining fleece(A) the same width and 3 inches bigger on the length.

Sew A into a tube and sew B into a tube. Put the lining in the outside so both seams are inside and fold the ends of A 1 1/2 inches over the outside tube and sew. No need to turn raw edge under--fleece doesn't fray. You have a tubular blanket with a contrasting border on top and bottom.

You could buy a decal of some sort to decorate it or even embroider his name on it or paint it on with fabric paint--just make sure it's nontoxic. Any decoration that is sewn on should be put on B before you sew it

I think I would also use quilt batting inside the tube. That way it would stay open just a little making it easier for the pet to get in.