There are different type of SEO audit is more generic you need to ask what he wants:

Types of Audit:
On-Page SEO Audit
Off-Page SEO Audit
Technical SEO Audits
Content Audits using Google Analytics

*** Let's Say we go with a technical SEO audit:***
Then you will analyze a website using any tools such as screaming,semrush, or any other free SEO tools.

Run Site Audit:

Figured out the problems such as broken links, empty meta description, duplicate h1 h2 tags, images missing alt tags and so on

added them in a Excel sheets with URLs in it so clients can see and send to the developer to fix it.