Wondering how you can play your UMD games on PlayStation Vita? Sony's solution to that matter comes in the form of their UMD Passport program, which lets you get digital versions of your games for a price.
By using a UMD Registration Program downloaded to your PSP, you'll be able to tie UMD games to your PSN account. From there, you must pay a fee (current rates are 500 to 1500 yen in Japan) in order to download your game. Also, these digital PSP games can be played on PSP and PSPgo consoles, not just Vita.
Keep in mind once you've registered a UMD, that UMD can't be used with other accounts. Apparently Sony can track registered UMDs though it isn't known how they do this.
When you play a PSP game on Vita, you can toggle a few settings before booting up your game. You can make textures appear smoother and enable use of Vita's right analog stick. If a game supported the PSP camera peripheral, you can set that game up to use Vita's front or back camera.
Want to transfer PSP saves or other media to your Vita? Sony will provide a content management program for PCs that let you copy or back up data to and from your Vita in addition to downloading games from the PlayStation Store. A similar set of features will be available for PS3s through a future firmware update.