In your Settings app, go to General > Restrictions. Turn on "Enable Restrictions." Then, scroll down a bit, in that same area, and you'll see a line titled "Require Password." If you press on it, you'll be offered an opportunity to require a password immediately when you attempt to access the App Store.
Alternatively, you could turn OFF the "Installing Apps" option (further up that page). However, that will make it so the icon doesn't show at all (I think - I don't use this option, but I'm pretty sure the App Store icon disappears). So, if you can't see it - you can't buy apps...
Hope this helps.
Marilyn