The letter to Theo, below, is one of the famous ones because he describes his perspective frame. The best translation I could find for this letter is here: http://www.vangoghletters.org/vg/letters/let254/letter.html
I think to understand how Van Gogh used this device, it's best to read his letter because the descriptions of him using it, written by Van Gogh enthusiasts, don't seem to match what he said.
To sort it out in my own mind, I've looked at some of his work. He built the frame and wrote the letter in 1882. He said in the letter that it takes a long time to get the hang of it (I'm paraphrasing!) and that if you look through it without understanding how to use it, it's confusing.
Looking at this painting of fields, "Field with Flowers near Arles," which he painted in 1888, I think I can see how he came to use the frame for the perspective in some of his work. I've tried to diagram that here.
I see him walking around with this big heavy wooden structure, finding a scene he liked, and then making a painting of a portion of the scene. The frame would help him anchor the perspective even if the scene didn't contain all of the angle lines. It would also help him organize the composition. He might not have done it this way, he may always have centered the frame on the view. That is how it is usually described, with him painting or drawing from the center of the frame. But I don't think he always did that. I think he used it in lots of different ways to get the effects he wanted.
This is just one small bit of the perspective conversation...it's most artists' great struggle!