Actually, it doesn't require any care and feeding.  Just acquiring and hatching.

First, go to Alderaan.   Get a MGGS from the vendor in the Juran Mountains, if you don't already have one. 

The MGGS is usable for datacrons, and can be mailed to your alts, or put into Legacy storage.



Taxi to the Panteer Refuge.  (Second closest is Wardpost Hurne)
 


Travel to Castle Panteer, and go around to the south side. (you can shortcut in the river to avoid being shot at) Look for the magnetic point, and use your MGGS.

 

Pick up your egg! I've read that this has a four hour respawn.

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Now, head for Tatooine! Taxi to Dreviad Outpost in Jundland. Fly around on your speeder until you find a moisture vaporator with a glowy blue panel at the base.  There are a lot south of Dreviad Base.  And one in Anchorhead.   Imp side there are a few northeast of the speeder plaftorm in Mos Ila.  Click on this to get the buff "Refreshed and Sustained."

 

Once you have this buff, taxi or otherwise travel to the Dune Sea. Speeder all the way across to the south west to the Czerka Compound.

 

Walk under the big solar collector and wait. It takes at least a minute.

 

Viola! You have an orokeet!