There are some steps in conducting internal audit that are applicable to any process and they will prevent you from missing something out.
First thing you should do is to review the documentation related to the production process, meaning all procedures, SOPs, records, etc. This will help you perform a second step and that is to develop the audit plan where you will define the processes you want to audit, the people and functions you want to interview and precise timing for all this. Then, you should conduct the audit according to the plan. Since it is your first time to perform the audit it is recommendable to create internal audit checklist for the production process and list all requirements that you need to audit.
Once you finish the internal audit, you need to create an internal audit report and to deliver it to relevant authority in your organization.
If you noticed some problems or nonconformities during the audit you will also need to perform a follow-up to ensure that the problems are resolved, but this step will be taken in agreements with the top management.