The layout of the post should look like this:

The 'Report Post Button' is highlighted in this case.
When you click to report a post, it brings up a new page asking for a reason. Fill it in with a descriptive reason of why you're reporting this post. Standard reasons for it could include racism, personal attacks, or perhaps the content of someone's signature image.
This new page should look like this:

After you report the post, it will take you back to the original post you were looking at.
At this time, a new thread is started in a limited access forum - Reported Posts, with the reason you've given and a complete quoted copy of the post reported for posterity. This flags it up for the Admin Team, Supermod Team, and Advisors where it can be discussed to find a proper resolution.
Generally, action is taken within the next 10-20 minutes after the team comes to some sort of accord with 2-4 people agreeing a course of action. Occasionally, the dispute is a bit more complex as we discuss the best course of action in a situation. Oftentimes what might be offensive or reportable to some people, is perfectly permissible in a broader sense of scale.
A member of the Mod Team will then let you know what action, if any has been taken.