View Solution

Edit:
Many updates, DLC, and patches later after this post you can now download the neural patterns and save them till you get the required technology to upload.

While exploring your science ships will come across the researchable quest "Limbo". DONT research it. Its easiest to wait until you have Synthetics tech unlocked. Once this is unlocked research it, then choose the option to upload their neural minds into robotic bodies.
You then get choices:
1) Tell them to leave your empire (they will go away and MAYBE start a new empire somewhere else, becoming a new species called "The Awoken")
2) (PREFERRED) Tell them to stay they will colonize a random world within your border, the planet will start off with 3 synths pops.

~ If you can build Robots (but not Synths), the aliens get uploaded into Robots and become non-sentient... you gain a single Robot pop, that's it.

There is also the rare chance a Fallen Empire may give you the neural patterns instead of finding it.