In theory, 24-hour time shouldn't be that complicated -
If I remember correctly, to convert to 24-hour time, just add 12 to the P.M. hours starting at 1:00 PM:
8:00 AM (morning) simply becomes 8:00
12:00 PM (noon) simply becomes 12:00
1:00 PM becomes 13:00
8:00 PM becomes 20:00
...etc.
To conver back, any hour larger than 12:00 (i.e., all the goofy, unfamiliar 24-hour times) should have 12 subtracted from it:
14:00 becomes 2:00 PM
21:00 becomes 9:00 PM
9:00 simply becomes 9:00 AM
12:45 simply becomes 12:45 PM
...etc.
(I don't remember quite what happens at midnight with 24-hour time, though - I've never had to worry about it that late at night before. I'm pretty sure it's 24:00, though I wouldn't discount the possibility that I remember wrong and midnight is 0:00 ...
)
In practice, though, when faced with a 24-hour time figure I stop, blink at it, take a moment to figure out what it is from its context, remember there's a way to convert it, try to remember how to convert, slowly do the math in my head, double-check it, suddenly get the eerie feeling I don't remember how to tell normal time after all - it's anything but an intuitive, automatic process for me. If I were in the military or something similar, though, and had to deal with it on a daily basis, it would probably be something I'd get pretty good at (and, more than likely, you would too.) After all, I assume the military prefers 24-hour time because it's actually less complicated and confusing, and thus easier to communicate accurately with, than 12-hour AM/PM time.