PS Vita won't support PSOne/archive titles at launch. You will need to wait.
From Gamespot:
Japanese PS Vita FAQ page reveals upcoming handheld will not play
archived titles initially, says more details will be revealed later.
And from the Playstation Blog:
Q: Is PS Vita compatible with other PlayStation platform games like
PS3, PS2, or PSP? Do you have any plan to support other PlayStation
platforms in the future?
A: Users can play supported digital PSP
titles and supported minis. In regard to PSone classics titles, we
will announce further details when they are ready. PlayStation does
not have plans to make PS Vita compatible with PS3 or PS2 titles at
this point.
Update: PSOne Classics will come to the Vita August 28, 2012 (Joystiq)