How do I install an SSD drive that comes without a casing in a desktop computer?

This is an mSATA SSD.

To install a drive like this on a system without an mSATA slot, you'll need an mSATA to SATA 2.5" adapter. This StarTech unit was the best I could find from a cursory search on Google.

Do not confuse this with the M.2 form factor, which is (usually) narrower and longer. M.2 also differs by having one mounting screw hole (cut as a half-circle on the edge of the board to save space) at the end of the card, rather than the two on mSATA.