What you have there is very likely what is being called "mSATA". Basically, it's SATA on a mini-PCIe slot. I very much dislike this because they're not really compatible in any way whatsoever. They just re-used the connector because it was convenient. It would be like putting Ethernet on a USB connector "because we had a lot of them laying around" (hey, kinda like the JVS IO "standard").
If indeed this is mSATA, you could theoretically just get a special cable to hook it straight up to a normal SATA port, but I'm not sure anyone makes one. They're intended to get dumped into specially designed laptops. You could try hacking up a SATA cable and soldering it down to the right places on the connector, but uh, yeah. Good luck: it's small, and it has to work at 3GHz.
If this is NOT mSATA and is in fact a real mini-PCIe card that just happens to have an SSD implemented on it (these were made, but I've never been able to find one - I'd kinda like one for my laptop, actually), then there's no way to hook it up to a standard SATA connector (because it's not SATA), but you could either put it in a standard mini-PCIe socket or buy a mini-PCIe to PCIe 1x carrier card.
Whatever you have, it's a Dell part. Dell can probably tell you what it is specifically, but they probably won't give much help beyond "put it back in your Mini-9".