I'll describe what we do here in our internal audit. We look at a one of the defined processes, as per the organization's process definitions. I'll say "Production" as the example.
We look at the documents related to the process (what does it say in the manual, procedures, work instructions).
We identify the clauses in the standard that apply to the process (hopefully defined in one of the previously mentioned documents, else, defined in the internal audit documents).
We re-familiarize ourselves with the requirements from the standard for the process.
We pick out some of the key concepts that the documents describe (like take the output of contract review and convert it into a work order).
We sample these work orders to see that they were issued following the organizations documents.
We review the activities involved in fulfilling the steps as detailed in the work order.
We ensure that the process is following the requirements of 1) the standard, ISO 9001, 2) the organization, and 3) the customer. We look for conformance to requirements (not looking for non-conformance), and in the process, if there is something that does not meet the requirements, we will identify this as non-conformance.
The other method worth noting is the "source audit" approach. Source audits in this context are those types of audits conducted by the customer. Review the contract, review the planning, review the activities, review the outputs of the activities, and review the final output to make sure it meets the contract requirements.
Example: Contract/PO 8675309 is for 37 widgets, revision "X". The contract/PO states delivery dates, documentation requirements, and potentially post-delivery requirements. If the documentation requirements call for a detailed inspection report, look at the inspection report. If the contract states the material used must be DFARS compliant, review the certificates for the material. If the material is to be processed per a specification, review the spec, the certs, and the method that the organization confirmed the material meets these requirements. If the contract says to package the delivered product in a box with a pink bow, we look for the pink bow on the box....
I hope that helps.