Before we jump into the video I created (see below), remember that the role of a site collection administrator is a very critical one in any organization. These types of admins aren’t SharePoint server administrators with authority on the actual web servers, but neither are they mere subsite owners or end users.
Usually, they’re power users. That makes this responsibility an important role in governing and administering SharePoint sites.
One of the misunderstandings people have is the belief that if you’re a top-level site owner in a site collection, you must be a site collection admin as well. Not true.
A site owner (also referred to as a subsite owner) has admin privileges on a site (which very well could be the top-level site), but if you go to the Site Settings page and don't see the Site Collection Administration section, you aren’t the site collection administrator.
In my opinion, SharePoint server admins should be very careful about who they appoint as the site collection admins, since that's a heavy responsibility that shouldn’t be taken lightly.
Also, you can’t take a person's rights away from seeing all of the information in the site collection. The site owner might go ahead and remove all security groups from a site, but this person will still have access to all data (and that's a feature, by the way, not a bug).
The video “Setting up Site Collection Administrators,” shows how it's done and also gives you some tips, tricks, and best practices along the way.
Asif Rehmani is a trainer and consultant primarily focused on SharePoint technologies. He is a SharePoint MVP and MCT. Asif is the principal contributor for the SharePoint Videos website, which provides SharePoint education for all levels of SharePoint users, developers, and administrators. Asif also provides in-person and online SharePoint training through Critical Path Training.