How can I straighten up a leaning vinyl fence gate?

Generally for a gate to lean (face is not vertical,) the post it's connected to is leaning, or its hinges have moved.

As such, re-setting the post or repositioning the hinges may be required, depending what the root cause is.

If the gate is sagging (face is vertical, but the free end is much lower than the hinged end) there is an additional possible fix, which is to run a support wire from as high as possible on the hinge post to the free end of the gate - usually this wire will incorporate a turnbuckle to allow it to be adjusted to pull the free end of the gate up until it's level.