Ensure that the current application supports dual analog stick operation.
If so, access an application that supports dual analog stick controls and check that the analog sticks are calibrated by rotating them in a circular motion before releasing them. If they are properly calibrated, they will automatically be reset and adjusted to their optimal position.
Some PSP games, PS one games and minis do not support dual analog stick controls.
Check if the analog sticks are enabled for the current game by accessing the In-game PlayStation Vita Menu (which is only accessible when playing PSP games, PS one games and minis).