Historically, most darker beers before the advent of the drum roaster have had some level of smoke in them, created by drying grains with direct fire normally.
The only difference in the smoky beers of today is that the method is being used intentionally to impart a smoky flavor, allowing even lighter beers like IPAs to be smoky.
In order to create these beers, the malts used are dried using smoke. These grains imbue phenolic smoky notes when they are used in the mash.
I think the easiest way for someone to ease into smoked beers is probably a smoked porter, where familiar flavors meet the complexity of added smoke.
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