I am wondering at what reputation the review button "comes alive".
I am happily reviewing from my Stack Overflow profile. Thought that came at 1 reputation, but guess not.
Assuming you're talking about http://stackoverflow.com/review, the minimum reputation needed to do anything is that required for down-voting. At this level, you can review First Posts and Late Answers.
Other types of reviewing require substantially more, based on the reputation required to do something useful during the process. As shown, queues that aren't available to you yet will appear grayed out, with the reputation required noted below them.
The expectation here is that you'll spend some time learning to use the site yourself before jumping in and trying to help others.
The "review" link should already be available to you now. According to the Privileges page on New User Restrictions, this is removed at 10 reputation:
Of course, many of the features are geared towards users with at least 125 reputation:
NOTE: The information on the Privileges page may need to be updated. According to Shog9, the "review" link is available at any reputation level.