DH said that the device should have its own power lead as it needs 12 volts of its own to work.
Certainly not 12 volts.
Unless it's a very elderly hard drive, it will only need one USB connector to both power it and transfer the data.
However, some 2.5" caddies come with those funky Y-shaped cables that have two USB plugs. That's in case you do need to put one of the aforementioned elderly drives in the caddy, or in case your laptop is a bit naughty and can't deliver the full specified power out of a USB port.
A USB port should be able to deliver 500 milliamps of current at 5 volts. That means it can't power devices which consume more than 2.5 watts. So to power devices that need up to 5W, or to deal with naughty USB ports that can't deliver 500mA, you hang them off two USB ports and take the power from both.
However, only one of those plugs carries data.
If you have a caddy which has a Y-shaped cable, then only one of those plugs will have the data leads connected. Normally, it's fairly obvious that one plug is "closer" to the disk caddy: the long lead goes straight into a plug, and then a thin lead comes out and goes to another plug. You want to plug the USB connector that has two leads, probably one thin and one thick, into your computer. Ignore the one which has just one lead, probably a thin one. If you just plug that second one into the computer, little will happen.
Alternatively, plug both of them in and have done with it.