A covered repair has three stages most owners treat as one: the drop-off, the work, and the pickup. A service contract adds a fourth stage that gets almost no attention, the close-out, which is the paper trail proving what happened after the car left the lot. If the close-out is sloppy, the next claim is harder to make and the next dispute is about what was never written down.
At the drop-off
Tell the service advisor what you observed, in your own words, and ask that the symptoms be written on the repair order as you described them, not only as the shop interprets them. Get the repair order number, the advisor's name, and the odometer reading the shop logged. Ask whether the shop will contact the provider directly and whether it will wait for the provider's approval before starting work. Those answers decide which of the later steps you will have to handle yourself.
During the work
If the shop calls to say the problem is bigger than the first diagnosis, ask for the new findings in writing before you say yes. Note who approved the extra work, the time you approved it, and the reference number that came with the approval. Keep any callback note with the repair order. A verbal approval that exists only in your memory is the weakest link in the chain.
At pickup
Read the final invoice before you pay anything. Each line should match work you approved. Ask the advisor to mark which lines the provider is covering and which lines you are paying, so the split is on paper. Confirm the odometer reading. If you want the replaced parts back, ask for them at the counter, not after you have driven away. Ask what warranty the shop gives on its own labor and parts, and ask that the answer be printed on the invoice, because a spoken promise is hard to hold a shop to later.
After you get home
Put the invoice, the repair order, and any approval notes in the same folder as the contract. If the provider has an online account or claim portal, check that the claim shows the work as complete and that the shop's order number matches the number on the provider's record. If there is no portal, or it says nothing useful, call, ask for the status, and write down the name of the person you spoke with and what they told you.
The close-out takes little effort spread over a few days. Skipping it saves you nothing, and it leaves the one repair you most need to prove sitting on a thin record.