Oh, this dreaded question. I will do my best.
I have come to the conclusion that I am a very slow thinker. It takes me a while to process information and come up with a way to verbalize it. I might intrinsically understand something in my head, but won't be able to explain it. Going from those two things takes the longest.
I am very much an auditory learner, supplemented by visual. However, there is something very interesting with me being an auditory learner; I am terrible with language. As an example (and this came up recently off the forums), I can't understand anything outside of plain english. What I mean is, writing written in modern english (shakespere style if you will) is near impossible for me to get. I have to read it, reread it, then reread it again and again before I can start to get it. It's very hard for me to understand unless language is explicit and clear. So as an auditory learner, I am actually based in sounds, not words.
I remember what people say to me very easily. Lecture is needed in school otherwise I struggle. When I remember what people say though, it is in their voice, and how they say it, not what they say. If their voice is distinct enough (and often it is), I will remember how they say something, the tone, speed, etc. From that I basicly hear a rythym with it, a tone, a style, and I can then retain the words they say, because they are actully said a certain way. What proves this to me, is I can hear or repeat what someone has said to me clearly, but not actually understand the words they have said. It was just a tone, I remember the tone, but not the words. This form of remembering and thinking is both very useful and very diffucult at the same time for me. Sounds can make me remember almost anything, and I am often surprised at the deeply forgotton memories I have had that I did not think about for year, which were reemerged by sounds.
I supplement the auditory with visual. I create images and figures in my head as I am explained to, but this is back processed. I am not really aware that I do this, it becomes apparent after I have walked away (more on this later). The visual is supplemented because the sounds and notes link to the images I see (it might be a graph I was shown or something, or created on my own), and each sound word and note will cause me to link to the image. So really it just is another way information is stored.
This also brings me to another point. I am a very rigid thinker. I can not think about more then one thing at a time. I must start a thought, and get it to a point where I can let it go before I start something else. If I don't I will lose that thought. The logic to where stop points off is unclear to others, but it makes sense to me. Unfortonately this means I can not explain it. I also think very "completely". There really is no grey area when it comes to thinking with me; all or nothing. I realised that nearly everything I think about, must be done to such a complete level that I must be able to then take that thought, and explain it to others. I don't try to do this, it is automatic. This is why a lot of people have the impression that I am really smart (which is very over estimated by many people), because I can often explain things with good clarity. Its just that, that is what my style of thinking does, it's slow, but very complete. This further creates this strange disparity between my thinking and language. Because for me to explain I must rely on language.
In short, I am neither left or right brained, I balance both, and I am a very slow but complete thinker, based in the auditory (but not language).