Well, the pilot instruction missions originate from mission computers. I believe you first encounter them in the very first system you start the game in, but I could be wrong.
Just do as many missions as possible; believe me when I say it'll take a Loooooong time to get to the fighter. However, if you'd gone through the game really really slowly (e.g. mapped out every frigging system in the galaxy before advancing the plotline) and snapped up as many bar missions as possible, you'll get the fighter. Keep in mind it is utterly impossible to finish the game w/o the fighter.
This mission, it involves famous scientist stuck on plague ship she's just barely managed to get out of hyperspace, yes? In case you didn't notice, this ship moves absurdly fast. Here's how I did it:
As soon as you lift off, point your ship south and go full throttle, full afterburner immediately. Maxing out speed and manoeuverability upgrades useful here. When the ship finally does jump in, it will (unbelievably) STILL outrun you, even at max speed! This is where the tractor beam comes in! Simply lasso the ship, disable it (CAREFULLY! A missile will acutally blow it to atoms), then slowly drag it to a halt before bording.