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When I read Scripture I try to understand what it says and means. I try to take the context into account - book/section/paragraph. If I'm studying, then the historical, grammatical and literary aspects can help to enlighten my understanding or even change it. What I'm saying is that the details of reading and study are really not much different than how non-dispensationalists approach Scripture.
I have discovered that what does make me different as a dispensationalist is the emphasis on progressive revelation. I know there is a lot of talk about literalness, but trying to define literal is a lot like trying to handle a wet fish. There are references to a sine qua non, but even there the number varies from 1 to 7. In the meantime lots of dispensationalists who have never heard of these things plug away at reading Scripture through a dispensationalist lens. I believe that somewhere along the way, the idea and emphasis of progressive revelation was communicated, we buy into it as a presupposition and that shapes how we approach Scripture - at least in the big sense.
The progressive revelation approach to Scripture gives rise to just about everything we hold as dispensationalists. For example, God promised the land to the nation of Israel, then when they are in the land, God promises Israel a future restoration - particularly when they are about to come under judgment. It seems arbitrary to us for anyone to separate "judged Israel" from a future "restored Israel" when we see them as the same nation. Its seems arbitrary to us when someone says that the "land promises" have been substituted for something more "spiritual." And its not that non-dispensationalists don't believe in progressive revelation, its just that they don't put as heavy an emphasis on progressive revelation (as Walter Kaiser said).
So for any non-dispensationalist who wants to understand dispensationalists better, I would tell them to put on a pair of heavily emphasized progressive revelation glasses, then start reading Scripture in book order.