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