For this you simply need a laundry basket, pillow, about a yard and a half of fleece or other material, and a leash.
Step 1: Dog Car Seat
I happened to find when i went to the store that both laundry baskets and pillows were on sale, Kaching! They also had those fleece throw blankets on sale for like $2.88 so altogether I spent like $8.33, though I already had a spare leash at home.
For my car and dog this all worked well, if you have a smaller dog or larger vehicle, you can also use belting material to make straps to attach the pet seat to the car seat allowing the dog to see out the window. For an example of what I'm talking about check here: http://ecx.images-amazon.com/images/I/51%2B9UVbZsjL._SL500_AA300_.jpg
Step 2: And We Begin...
Lazy way: Put the pillow in the basket and simply drape the blanket or fabric over the pillow to make it softer and cover the vent holes.
Or if you want a more finished look you can measure the sides of the laundry basket and actually sew the fabric to make a pillow case with walls type of deal. It doesn't take a genius to figure out how to make that happen and I didn't take picture of the sewing bit.
Step 3: Keeping Fido Safe
Now you could get all fancy and legit, but it's going to be hidden by the back of the car seat anyways so who cares.
I simply took the leash threaded it through the basket and then through the handle an voila! Pooch, or kitty, stays in their seat and safe. I also take the added measure of seat belting the seat in place to ensure it's not sliding around.
Annnnddd you're done, Congrats on a fancy new cheap seat for your best friend.
The final image is the finished product. My dog Lucky Jack is laying in it before I had sewed the fabric into its shape, I just wanted to see what he thought of it.