How do I test a circuit breaker out of the circuit box, and still hooked up to the circuit box?
It sounds like your circuit breaker is tripped.  Often they don't look much different between tripped and one of the full on or off states.  To reset these types of breakers, you usually need to manually flip them all the way to off, then back to on.  You can't go directly from tripped back to off.

If you remove the breaker completely, then it should look just like a switch electrically.  There should be a short accross its terminals when on, and open when off.  You should be able to test this easily with a ohmmeter.

In the panel, you can look for the AC voltage between the output of the breaker and neutral.  That should be your line voltage when the breaker is on, and zero when off.  As long as your voltmeter is set on the appropriate voltage range for your wiring, nothing should blow up.  The meter is a open connection as far as the house wiring is concerned.  You have to work at it to blow something up, like put the meter on amps scale or something.

Testing whether the breaker trips when it's supposed to is a whole other issue, but you don't seem to be asking about that.