On this page of the FNAF Security Breach guide, you will find a walkthrough for the Parts and Service mission. Here we supplied a detailed walkthrough for the task.
The mission begins as Freddy is kidnapped by Moondrop. You can't help him right away - first, you need to obtain the right Security Badge (Warehouse mission is dedicated to this)
When you get to Parts and Service you will witness Vanessa talking to Freddy. After a while, when she leaves the room, you will be able to go inside.
First, go to the computer and choose an upgrade. This way you will be able to get to the repair chamber.
You'll be able to connect Freddy's head there. The whole process involves a mini-game in which you have to click on the highlighted elements.
When the whole process is finished, leave the chamber and interact with the computer again. This way you will free Freddy and the quest will end.