Just don't bother...
Unless you live with them. Then good luck.
Throw a CPU core at Folding@Home or something & just imply the rest of the hardware is doing the same.
It's hard enough explaining bitcoins to high level geeks who understand all the concepts.
to avoid alot of hassles and arguments, build a computer that's aimed at mining, but running other stuff (folding@home, teamspeak/game server, whatever) too
then ask your parents to place it in the garage or something (so that its not on ur bedroom) and tell them that it needs to run 24/7 for your friends and curing cancer (best excuse ever imo
then after a month or 2, when they inevitably ask you why theyr power bill has gone up so much, tell them about bitcoin basics (its a new currency, blablabla, practically the same as dollars, euro, other currencies etc etc)
if they dont believe you still; show how much money you made already and offer to pay the complete energy bill for the time period (if your miner generated enough that is, otherwise just repay what your rig used)
then you'l have proof that its not a scam and that you can make money with it
then explain why you did it behind theyr backs (parents can be such digidodo's sometimes
sure, its sneaky, cloak and dagger style and all, but imo the best way to handle things without too much fights. this way you'l only have one, in wich you have the advantage of knowledge, proof, and strong arguments