I don't use anything that has Capital Letters, per se. I borrow from a lot of things I read and see, from working trainers I admire, to performance trainers, to behavior modification experts.
What I don't do all that well is absorb a single method or theory from end to end because I tend not to like extremes that any method is carried to, in an attempt to apply it strictly. What I mean by that is, I don't find it practical to use 100% "positive" methods helpful when training a dog for working livestock.
I don't even train all my dogs the same way though. I've got a foster dog in recently that I HAVE gone 100% positive with. She's not destined to be a working dog, so it's lots of fun to play with. From there, I worked with my puppy until recently using the same methods, with one small difference - I did train him to recognize one gentle verbal correction.
For household manners, I tend to use R- a good bit. Time is much too short around here to fool with clickers but my pockets are always full of treats and I "mark" things I like, verbally, and treat. Or in Gus' case with a verbal signal. :)
For instance, Sam recently started busting through doors when they were opened. Very bad habit for a stockdog. As soon as I'd grab the knob, he'd press his nose against the doorjam, ready to charge. So I'd walk forward, touch the door, then backed slowly up into the room. He looked at me the first time like I'd lost my mind. Then he followed me until he was walking behind me, but "ahead" of my motion. Immediately I walked forward and praised him, but the second he charged past me, I backed up again.
We repeated this until he decided the best thing to do was to stand about two feet from the door and wait for me to open it. 
But to train him to stay in a crate with the door open until given permission to exit, something we are starting this week, I open the door and then shut it quick if he sticks his head out. That's slightly aversive - P+ - but he can elect to avoid it next time around. Many smart dogs take the above lesson (at the front door), and hesitate at the crate door, so the door closing randomly isn't a surprise.
Then the dog learns that if they hear the cue releasing them, the door always stays out of the way. It takes a couple of rounds of the dog standing there going, "Really? No kidding?" but this sort of thing happens while working livestock too, so it conditions the way they learn to accept this type of lesson. Ie, "Pressure won't kill me." Also, to think before doing stuff and not blast around like a reactive idiot.
If I had any overall philosophy in mind, I aim to help my dogs develop a sense of being a part of the team and working with their natural inclinations - usually along breed lines.
I've worked with people who got into the dominance thing and it was really ugly. It's possible to "get away" with applying it to the limited demands of companion animal behavior. But when you start warring with high powered instincts, well, I witnessed things that were pretty close to abusive and I'm sure most here would put them squarely in that category. 
But even so, here again you can't dismiss a methodology 100%. I used to get dogs that were horribly spoiled and before anything could be done with them, they did have to know they couldn't push people around. I don't think dogs naturally seek control but a clever dog can learn to manipulate its surroundings the way it likes. These are great dogs with loads of potential but the first thing they have to learn is that they can trust me to make the decisions.
In general, I use extremely passive methods to convey this, but I've noted discussions here that indicate that even those would meet with disapproval. "Being a tree" just out of reach while a dog I'm walking throws a tantrum trying to reach me to bite me, for instance. I use collar corrections to train certain types of sulky/aggressive dog.
But 90% of what I do is providing dogs with expectations, a regular way of life and something do do with themselves. I have a strong belief that most behavior problems stem from the dog feeling out of place. Dogs love routines and our modern chaotic lives don't do them any favors.