Basically, it boils down to adding your Google account to the Android device of whoever you want to share apps with. App sync will do the rest. And if you don't feel comfortable sharing your personal account - okay, you probably hate the very idea of it - one can simply create a dedicated app sharing account they can switch to any time they make a Google Play purchase. When this account is added to respective devices, they can use all apps purchased through it. Could have been much worse!
Anyway, here's how to sort yourself out: