How do I get my character to float/boost up?

Here are all the ways you can control your character's ascent from the ground.

In Two-Handed Mode, pressing the jump button for a short amount of time will use up one charge of Wing Energy and cause your character to “flap” and boost into the air. In One-Handed Mode, a long press anywhere on the screen will function the same as the jump button.
Additional boosts can be performed while in the air to gain more height by continuing to long press the jump button until you run out of Wing Energy charges. Each boost will consume the equivalent of one charge of Wing Energy. Once all full charges are depleted, any remaining partial charge will be consumed for a smaller boost.
If you long press the jump button and do not have sufficient Wing Energy, it will have no effect. The game will give feedback indicating that you are out of Energy by flashing red where Wing Energy charges are normally displayed at the top center of the screen.

You can increase your total Energy (the number of stars on your cape) by finding Winged Light scattered throughout the world, which allows you to increase the number of consecutive boosts that are possible.