Great advice from everyone above. Max was a squirmy puppy when it came to grooming. I trained him by waiting until nap time, then I would put him on my lap and massage and pet him for a little while until he was completely relaxed. I would then start combing him gently and continue petting him, talking to him softly, praising him. Eventually I tied grooming to going outside for walks. Max knows he has to have his hair combed before we put on his harness.
Be calm and confident when you groom or take your pup to the vet. Dogs are very smart and will pick up on your anxiety. Practice several times a day and touch your pup all over from ears to toes so that he will accept being touched.
Praise and give rewards. He will get the hang of it.