What order should I teach my dog commands?

The basic commands that every dog should learn are: heel, sit, stay, and come.

Heel – With the dog at knee level on your left side and the leash in your hand, start walking with your left foot first as you give the “Heel” command, using the dog’s name. Hand out treats and positive reinforcement when he walks properly. If he doesn’t get the it right away, give the leash a gentle pull to bring him back into place and start again.
Sit – Simply hold a treat toward the back of his head as you say, “Sit” with the dog’s name. If your dog doesn’t, lightly touch his butt as you issue the command. Then treat and praise.
Stay – Start with your dog in the sit position. Standing in front of him, show an open-palm hand command as you say, Stay. Keep eye contact and leave him in the stay position for 30 seconds, then release him with the word, “Okay!” While you practice, have him stay for longer periods as you stand farther and farther away.
Come – Hook up a non-retractable leash at least six feet long to your dog in the “Sit” position. Pull gently as you say, “Come,” and the dog’s name in an happy voice. When the dog comes and sits in front of you, shower him with praise and give him a treat.