How should one say times aloud in 24-hour notation?
The armed services (and their veterans) really have this engrained in my mind as such:
Rendezvous at 0600 [O-Six-Hundred] hours!
Drop point is X degrees north, at 1200 [Twelve-Hundred] hours!
Otherwise, where more precise in terms of declaring minutes, you can just split them and speak each unit of time individually:
Your meeting is at 1530 [Fifteen-Thirty] hours.
Your meeting is at 1812 [Eighteen-Twelve] hours.
The hours here, it might be argued, is redundant or even inaccurate, but that doesn't dictate the occurrences (or exclusion of such) in speech.
You could go the quarter to, half past route, but this is an interchangeable method of speaking time, not exclusive to verbalising time in its 24-hours form.
Since o'clock is an abbreviation of of the clock, I guess that technically you could speak in this manner in terms of 24-hours, such as: 15 o'clock. But this might sound a little peculiar to most. If we look at the definition of o'clock from TheFreeDictionary then it kind of indicates we would be playing it safer to use another form:
Of or according to the clock: three o'clock.
According to an imaginary clock dial with the observer at the center and 12 o'clock considered as straight ahead in horizontal position or straight up in vertical position. Used to indicate relative position: enemy planes at 10 o'clock.
used after a number from one to twelve to indicate the hour of the day or night
(Mathematics & Measurements / Navigation) used after a number to indicate direction or position relative to the observer, twelve o'clock being directly ahead or overhead and other positions being obtained by comparisons with a clock face
If we do decide to use the 24 o'clock approach, then it's just redundant, if nothing else; consider the note on relativity to the face / direction. Since, regardless of the numbers being bigger, we don't have to (necessarily) do any extra laps around the clock face to arrive at the specified location - but in cases where AM and PM might not be clearly implied, it could serve to do that.
In 24-hour notation you never say o'clock. Say the value of the hours part first, then the minutes.
If the hours or minutes are less than 10, say Oh (for zero) first.
Non-military people don't usually say the "Oh" before hours, especially if the minutes are non-zero.
If the minutes are zero, say (hours) hundred. People (esp military) often say hundred hours (esp if the hours are less than 10).
0700 - Oh seven hundred [hours]
0701 - Oh seven Oh one
1500 - Fifteen hundred.
1503 - Fifteen Oh Three
1510 - Fifteen ten
1559 - Fifteen fifty-nine
I think there's a big problem with 1000. Nobody much likes saying ten hundred, but I don't know how you get around that if you must speak in 24-hour notation. Most people just say Ten o'clock and forget it.
In practice many of us mix traditional and 24-hour because (like you, I suspect) we have digital displays and can't always be bothered to mentally convert, say, 1550 into ten to four before speaking. You have to decide how far you want to take your own usage (partly dependent on how good you are at mental arithmetic :). I recommend reverting to traditional for 1000 at the very least.
LATER - Since posting this I've realised American (not British) usage accepts fifteen o'clock, for example, for 'exact hour' times after midday. But if you follow that link it's obvious this usage has fallen off significantly since the war. And if you switch the "corpus" to British, you'll see we've never used it enough to even show on the graph.