Process verification is covered in the AS9100 Rev D specification in clause 22.214.171.124, production process verification, and requires that you assess the ability of your processes to meet the product and service requirements by taking a representative item from the first production run to verify that all the production processes to create that item meets all requirements. This is also called first article inspection (FAI), and for more information you can use AS9102 which is referenced in Annex C (remember, AS9102 is a suggested tool, and not a requirement of AS9100). The AS9100 standard does not dictate what forms or records to keep for this, but if you use AS9102 there are forms included in there. The decision of what records to keep are up to your organization and your customers.
As for equipment verification, the AS9100 standard does not include requirements for verification of equipment that you use in your processes outside of the clause above. If you are talking about making equipment, clause 126.96.36.199 of the standard discusses planning tests for validation and verification of the product or service you design. If you were talking about equipment verification as your product or service, then this section talks about the requirements for the test plans and test procedures, but also does not have any requirements for the format of the documentation.