Take the red lead from the multimeter and plug it in the 10amp DC section, put the multimeter on the 10amp setting aswell. Go to your battery and leave the positive lead connected, remove the negative lead the put the positive of the multimeter on the negative of the battery, the negative of the multimeter on a good earth. This should give you a amp reading. For a radio it will be around 0.10 amps. To see that the clock is using the power take out the power to it or the fuse and the amps should drop, if it doesnt drop by much keep unplugging accessories until you find the culprit.
EDIT: 0.10 amps is probably abit to high for the radio when its off, should be around 0.02 amps, which explains why my battery is draining after a week, damn lucas electrics :ranting2:
Just done a similar thing on my car as something was draining the battery, easiest way is to pull out fuses until the amps drop, if your boat has any.
Hope that made sense