Design, embellish and bedazzle your basic pattern pieces in whatever way works best for you. Obviously it helps if you can sew, but it's not entirel...
I think that no matter how you personally feel about dogs, we can all agree that dog costumes are hilarious. Yes, it's true that we are laughing at them, and not with them, but as long as they're willing to play along with it I don't think there's necessarily anything wrong with that.
It's actually pretty easy to make a costume for a dog, just as long as you keep a few basic concepts in mind.
By this I don't actually mean YOUR limitations. I mean the dog's. Let's face it: your dog does not really want to wear a costume. Dogs don't really want to wear anything at all. To demonstrate, here's a video clip of my dog, the first time he ever had a collar put on him. He doesn't understand what it is and doesn't entirely understand how his own foot works, but he knows he doesn't want this thing on his neck. So please keep in mind what your dog can comfortably tolerate when you come up with your costume idea. If your dog will not wear a hat, you should not come up with a hat-dependent costume.