Submissive dogs present an interesting challenge during training. Learning how to work with these dogs is key to helping them gain confidence and overcome their submission.
Understand a dog's body language - signs of submission might include that darling doggie grin you get when you walk in the house, ears laid back, tail between the legs, slinking close to the ground, and, of course, my 3-legged dog's favorite - peeing.
Understand submissive urination - many pet owners think the Rover is peeing in front of them to (sorry for the pun) intentionally piss them off. Understanding that submissive peeing is uncontrollable for the dog is necessary to help the dog get over this symptom. To help the dog become less submissive, DO NOT YELL at him. Yelling will only send him into a further submission. DO NOT look him directly in the eye. Pet him under the chin, instead of on top of the head. Ignore the dog when you first walk in the door - don't make him more excited than he is (submissive dogs typically will pee when excited too). After he calms down, get down to his level and let him come to you. Never tower over a submissive dog as you will only create more submission.
Vocalize your pleasure - use an incredibly happy voice when praising the dog. Give treats liberally and, most importantly, when training, only ask him to do what you know he can do. Don't give him a command that you're not 100% sure he will obey. Sometimes, this means that you might utter 'Sit' as you see him start to sit. Then, praise! Yes, it might seem silly but, every time you give the dog a chance to succeed, you strengthen his confidence.
Training on an Agility course - training a submissive dog in agility will increase his confidence many fold. And, you and he will get some good bonding time as you exercise together. In fact, any fun activity you can find to do (chase the stick, hide the treat) will help him gain confidence.