Maybe it could be a learning to control her new powers kind of thing. Like she tries to levitate a glass of water, but she ends up crushing it. Or she tries to turn and apple into an orange, but creates a giant crater in the center of Ponyville. Or she could try to teleport one of her friends, but they end up flying high into the sky creating a "My people need me, I must go to them!" moment. Showing her trying to come to terms with her new incredible power and making it so she can master it and still be one of the girls, only she happens to be the girl with the power to lift a building over her head.
Those of you who don't watch Game Grumps may not find this as funny as I do, sorry for that:https://www.youtube.com/watch?v=XBl9jVYRIB4
Edit: Also speaking of Twilight becoming an alicorn I found this comic just now and it gave me a few chuckles. For some reason I love it when the characters reference fanfics: