You fold it and insert it similar to how you would a tampon.
There are multiple folding methods - C-Fold, Punch Down Fold, 7 Fold, Origami Fold - I've no idea what you mean by "U" shape or the "E" thing, most people just use the straight up C-Fold but if you struggle with that look at folding methods and try a few to see what work best for you. Menstrual cups are not too big, your vagina is designed to allow a whole human being to pass through it, you have instructions on how to insert menstrual cups and online communities to help you if you're still stuck.
Once inserted they cannot be felt at all, and unlike tampons they don't increase cramps or cause dryness.
For the record the Divacup will only flip if it's not suited to your body, in which case you just get a different brand, but this very rarely happens. The Divacup also cannot attach to the vaginal wall, that's utter nonsense.
Examples of different cup folds - http://menstrual-cups.livejournal.com/453392.html
How to Use a Menstrual Cup: 14 Steps - http://www.wikihow.com/Use-a-Menstrual-Cup
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https://www.youtube.com/watch?v=QfHF0p7X4MI