How are operators of small UAS craft supposed to know about flight restrictions?
Information about current and future TFR areas is available from the FAA, even as an easy-to-read map. If someone is planning on flying a manned or unmanned aircraft, that should be on their list of things to check ahead of time.

As far as other airspace restrictions, we have a question detailing the different types of airspace. It would be worthwhile for a UAS operator to learn enough about reading charts to at least know the airspace in the area where they intend to fly.

Another option would be to attend ground school or at least do some amount of self-study. Just as pilots need to know how to operate according to the rules of the airspace system, UAS operators could benefit from the education.