Depending on the drivers and your goals, you may be doing only an inventory or audit (I say "only" but it's still a major undertaking!). In that case you just need to know what you have, what types of content, how many of each, and so on.
If your goals are to improve performance or effectiveness of your content, you need to do an assessment--not just an audit of what is there, but what is it trying to do, are there errors, and is the content effective? So, an assessment is going to include an audit and then some diagnoses, recommendations, and a treatment plan.
Start with your goals and targetsThis step starts with the goals of the driving project--the initiative that raised the need for an assessment. There are cases where you are doing a content assessment simply as discovery--the assessment itself will catalog and potentially identify improvements you may not have thought you needed.
The reason you need to articulate the driving goals is to know what you will be collecting and analyzing during the audit. You'll also determine the scope of your assessment--do you need to analyze all the content or a subset? What information and parameters will you collect per asset?
The goals also keep the auditors on track--audits and assessments can take a long time, so you don't want to waste any time on unnecessary tasks.
Targets are particular metrics or rules you will asses--for example looking for blank Title tags or editorial usage violations.
Scope the audit or assessmentWith the goals enumerated, you can scope your project. What content has to be audited and what not? What information do you need to collect for the analysis? Do you need analytics and SEO data for each page or asset?
At the end of the scoping, you should have a database or worksheet defined to collect the data set for each asset--a content matrix.
Inventory the contentNow you have to do the work. There are usually no shortcuts--unless you are doing a simple inventory and can use your CMS or other scripting & crawling tools to automate the tasks.
Even if you are doing a complex assessment, you can often start building your content matrix with the basic inventory of content with automation. Then auditors can use the matrix to divide and conquer the rest of the data collection process.