Extract one or two telling symbols, features or images from the overall content, and build the poster around that. In other words, if you're advertising a music festival, you don't have to crowd the poster with images of bands, the venue and instruments. A stripped-down symbol -- such as a lone guitar -- or even a solitary amp, can communicate the same message.
Use the technique of portmanteau, the contrast of two simple, stark, juxtaposed objects. Portmanteu is a common motif in minimalism.
Limit your use of colors. Choose only a few colors; or even reduce it to primary colors, like red, blue and yellow. The DeStijl minimalists of the early Twentieth Century were known for their reductive application of color.
Include text as needed, but don't crowd the poster with excessive text. Say only what needs to be said. You can communicate additional details by leaving a phone number or website -- depending on the nature of the poster.
Use close-up imagery. Zooming-in -- either photographically, painting or drawing -- on an object, or part of an object uses the component to say something about the broader whole, without having to explicitly state "the big picture" -- literally, in this case.