I'd expect to hear it a lot in Japan.  When people are trying to decide on plans, or when someone is trying to figure out what's best to do in a situation, you can expect a lot of 「どうしようかな」s all over the place.   That's the example I hear most, but I seem to hear it about a hundred times a day in one form or another (especially the copula だろう).

The basic "let's ..." usage is easy but they keep using the volitional form in cases where it doesn't seem to make much sense to use it. But it's just a question of getting used to it.

Tae Kim has an excellent explanation on the volitional forum used in situations such as coupled with とする and と思う. Check it out: http://www.guidetojapanese.org/learn/grammar/try