You might think that, since the PS Vita is the PSP's successor, managing and transferring games, photos, and other content would be pretty much the same. But just as the PS Vita got a brand-new user interface completely unlike the PSP's and PS3's XMB, the way you'll access and transfer content is different, too.
Out With the Old
Transferring content to and from a PSP was a simple drag-and-drop process that involved hooking your PSP up to a computer via a USB cable and treating it just like an external drive. As long as you had the correct file structure on your PSP's memory stick, you were good to go on a Windows or Mac. If you wanted something a little more like media management software, you could download Sony's Media Go software free, and use it for everything from managing content on your PC, to buying and downloading from the PlayStation Store, to transferring content back and forth from a PSP. The biggest drawback was that it's Windows only (Sony management software has long anti-Mac history; their e-book management software for their e-readers is also Windows only and had been for ages).
It's also possible to transfer content--such as games downloaded from the PlayStation Store--to a PSP from a PS3, essentially by connecting the two via a USB cable, navigating to the desired game on the PS3's XMB, selecting it, and selecting the option to transfer. In both of these scenarios, the PSP is treated more or less just like any other external storage device.
In With the New
With the PS Vita, you will no longer be able to transfer anything by the drag-and-drop method. There is speculation among the gaming press and the homebrew community that this is another attempt to reduce piracy, which makes sense considering the big problems Sony had (or believed they had) with PSP game piracy, and the lengths they've gone to in trying to prevent it.
Instead, the PS Vita will use some software called Content Manager which is meant to do exactly what it says: manage your PS Vita content. Content Manager can be activated on the PS Vita itself, and you then use the touchscreen to access content on your PC or PS3 (once you're connected via a USB cable), and to transfer content back and forth from the PS Vita. This will certainly be a big help if you don't want to spend a lot of money on memory sticks to store all your games and save. Instead, keep them on your PC or PS3, then transfer them to your PS Vita as needed.
There's a catch though. While there may be a more complicated workaround, it looks very much like transferring to and from a PS Vita and PC will require the installation of something called Content Manager Assistant on your computer (it's a bit hard to tell from the online manual whether or not this software is absolutely required, or whether it's simply easier, but I'll update once I've been able to figure it out for sure). That's not a big deal, as it certainly makes keeping track of and organizing your PS Vita files more convenient. But, like other Sony content management software, Content Manager Assistant is Windows-only. If you're a Mac user, you may have to either use your PS3 (if you have one), or buy a lot of memory cards. (I'm hoping I'm wrong, and that it will still be possible to transfer files by connecting via USB and using Content Manager on the PS Vita itself.)