Data Vaults are located in space and show up as a purple ping when using the Lon-rang scanner. Once You have a ping just fly toward it till you find the Vault. They can be found in asteroid belts as well as in deep space all by there lonesome selves. They will show up on your radar and your map as long as they are inside one of your active sensor fields but can't be selected to set guidance too so you will need to use the long range-rang sensor to narrow down there position.

In order to get the data out of the vault you need to get the vault back online. To do this first get your ship close to the vault than get out of your ship. You will need a repair laser for this part. Look for panels that are lit up in red and say presser leak detected(see first image). Just get close enough to hit it with your laser to fix it. It will turn green and say status ok(see second image). Some of these will make the solar panels align with the sun while others will open small hatches that can contain other panels that need repaired or containers you can pick up. Ones all the panels are repaired one finale hatch will open.

Now that the last hatch has opened fly over to it with you scanner going. (Default key-bind is shift+2) You will hear the static on the coms as you get closer to the spot. You will see some broken wires with a red mess of lights above them, just point towards that mess and slowly approach until you get the data.