Once you reach Rank 8 Weaver will give you a broken spaceship. After your next shift Lou will contact you and give you the Ship Doctor program for your employee terminal to fix up the ship. With this program you will use parts you salvage from shipbreaking by selecting "Pickup" when you see them around. It's all explained in dialogue and pretty straightforward.
To complete the first level you must install a circuit and wires through the program, then the achievement will pop.
If you are having trouble finding parts you can get the "Scan Mode Objects" upgrade for your scanner to highlight pickup objects in purple, which helps immensely. Also on the ship selection page you can see what items can be found in each ship, then just grab what you need and end the shift. As an additional heads up: while this achievement is only for completing the first level, fully completing the career mode requires 100% ship doctor completion in addition to completing the story... just try to complete it as you go along and it's not too bad.