I'm tempted to say almost never, but I'll try to be a bit more objective.
Basic answer - in spoken and informal English, most native speakers use whom very rarely. This is because for most of us whom sounds excessively formal and rather old fashioned.
Nowadays it is normally only used after prepositions, but we usually try to avoid doing even that by putting the preposition at the end of the clause or sentence whenever we can. This, however, isn't always possible, and in these instances using whom sounds perfectly natural. The trick is knowing what these appropriate whom moments are.