Determining which of your two or more canine friends is the "alpha", or dominant, one is relatively straightforward if you take the time to observe the way in which they interact with one another.
As with any good qualitative observation, watching how your dogs relate to one another is best done over a period of time. Taking multiple opportunities to see how your pets behave (or misbehave!) will enable you to detect trends or patterns that will signal which is the leader and which is the follower.
If, over a period of time, you witness one dog:
-avoiding the other(s) or staying near you for protection
-requiring veterinary care on account of injuries sustained by the other animal
-refusing to eat with the other pet
-doing its business in the house, even though it was previously house broken (the fancy name for this is "submissive urination" or "pet enuresis" and it is quite treatable, given early interventions)
-doing the other dog's house chores such as fetching slippers, newspapers etc.
-letting the other pet sniff its dainty bits (but not reciprocating)
-yelping around the other dog
...then this is definitlely not the "alpha" dog.
On the other hand, if several (or more times) you happen to witness:
-one animal pinning the other to the floor in a WWE style wrestling match
-taking the other dog's treats, bones, toys or food without resitance
-urinating (outside) over top the places where the other pet has already attempted to mark its territory or to stake its claim.
-initiating eye contact and maintaining it until the other dog looks away (usually down)
-low growling
...then this is your "alpha" animal
Once you have established which animal is on which end of the power relationship you may need to address any severe imbalances. Your energy will be much more efficeintly directed into teaching the alpha animal the limits on how to interact with your other dog(s). Attempts at counselling your submisive dog or trying to help build its self esteem are rarely effective. If you manage to reign in your more aggressive dog, you will do a great deal to preserve harmony within your household and preserve your submissive animal's fragile sense of self.
You will find many good articles here on Helium to help you train your animal. Here's a good place to start with some general tips: http://www.helium.com/items/1034819-essential-tips-f or-better-dog-training Investing a few dollars in obedience classes, however, can reap huge rewards. Not only will your alpha dog learn some boundaries, but your more submissve animal may get a chance to be around animals that are even less outgoing.