L'affaire Snowden and (Computer) Security
Because of aggregations and some related issues that I'll mercifully not explain, another big part of classification is something called compartmentalization; you break the information down into related groups by project, or a target of interest, or by source, or by some technical factor like how it was obtained. There are also compartments involved with how the information can be transmitted, up to and including the famous guy with the briefcase handcuffed to his wrist.
Often these compartments have names that are literally words drawn at random from a pool of possible words. These are called codewords.
When someone tells you about something classified "above TOP SECRET" they're not quite telling the truth -- there is no classification level above TOP SECRET -- but what they mean is that it's information that has to be handled by special channels, or it's peculiarly sensitive, like information about codes and cryptography, or it's under a restrictive codeword.
Access to Compartmented Information
I told you we'd come back to the problem of determining if you're actually trustworthy; here we are. For a low-level clearance, like for CONFIDENTIAL or SECRET, all that's done is a National Agency Check. Basically they look at public records to see if you have a criminal record, or something similar.
For codeword information though, you have a much more thorough examination: they not only look at any open records, but they check back on places you've lived, and literally send people out to talk to people you've known in order to confirm that everything you told them is true, to check if you ever had any questionable ties (like joining a Tea Party group I guess), and to build up a picture of your life in order to look for anything that makes you seem untrustworthy.
Survive that and you then get interrogated by a specially trained agent while on a polygraph.
This whole process is very expensive, probably now upwards of a million dollars, and people who have a full polygraph clearance are quite rare.