Are there any guidelines for a beginner like me on when to use this technique (apparently known as Dutch angle, Dutch tilt, canted angle, oblique angle, German angle or jaunty angle), and the extent of the tilt?
You may check this: http://www.picture-thoughts.com/photography/composition/angle.html and this as well: http://digital-photography-school.com/using-diagonal-lines-in-photography/
I really love to shot with diagonal angle/lines. Hope this help you and let me know if not.
A big part of this can be to fill the frame with a subject. It also tends to give a more lively feel to the shot as it feels less posed and more active. It works particularly well in shots of dancing when you can also use it to really fill the photo.
You can see in a lot of the samples in that first article how the subject of the photo goes from corner to corner, which fills the shot and gives balanced details on either side of the subject. Generally, it is fine to use it any time it looks aesthetically pleasing. Use it when you want to focus on the subject more than the surrounding area. Thinking of a skyscraper shot for example, a normal horizon focuses on the structure as it relates to the skyline. Rotating the image so that it fills the frame focuses on the structure while still giving some background, while doing it purely portrait orientation would not really capture the background.
Similarly, use it when you want to show activity. In dance shots or even general atmosphere shots, this works really well. It grants an artsy, edgy feel when done correctly with subject matter that fits that feel. I shoot just about all shots that are trying to capture a party off angle or somehow using a diagonal. (For example, with formal dancing, the horizon may be horizontal, but the angles formed by people's heads form a diagonal across the image.)