Huh. I've just never installed any ad-based applications. If there's a no-ad paid version for a buck or two I'll buy it, otherwise, I just don't use it.
I never install anything that hasn't been reviewed.
If it's free, but not a gateway to a paid service, I check to see if source is available; if source is available, it generally doesn't have ads (and if it does, I can just build it myself and remove them).
If the above checks fail, I check for a paid, ad-free version. If such a version exists, that implies the free version has ads. If the price is reasonable, I'll buy it, otherwise I'll skip it.
Finally you have free-as-in-beer but not as in freedom apps, that don't have paid alternative or any other way of generating revenue. I just assume those apps are either encrusted in ads or scams, so I don't install them.
The Play Store is a wild west of crap though, so you have to be much more careful.