@cmac678, you are in the US?
I suggest something like a condensor microphone from radioshack.
Power it from 9V battery, connect its ground to arduino ground, and its output to arduino ADC thru an electrolytic capacitor.
Here's one wired up in a box from ages ago, I put a new battery & battery clip on it, thing still picked up nicely with a guitar amplifier!

The output of the capacitor will be at 0V and swing positive & negative - connect two 100K resisters like this: +5V to resister, other side to 2nd resister+capacitor+Arduino input, other side of 2nd resister to gnd. The Arduino input should sit ~2.5v with no mic input.
You'll have to play with the ADC outputs, see if you can get a decent enough readings away fom 2.5V (reading of ~512) to make a decision on. If not, may have to add some gain using a single supply op-amp and a couple of resisters.
You'll have to play with the ADC outputs, see if you can get a decent enough level to make a decision on. May have to add some gain using a single supply op-amp and a couple of resisters.
http://masteringelectronicsdesign.com/how-to-derive-the-summing-amplifier-transfer-function/Use a circuit like this instead - the capacitor output will be V1 and V2 will be the junction of the 100K resisters. Or a trimpot! Then you can dial in the voltage needed to keep the output at 2.5V while adjusting the gain needed to adust mic sensitivity.
I'll see if I can find you an envelope follower circuit as well, that might come in handy if your ADC sampling loop doesn't run fast enough to see the hand clap with this mic.
Gotta get to bed tho, darn day job ...