Third-hand smoke can cling to fabric, skin, furniture, carpet and other surfaces including car dashboards. The exposure to children is most concerning because they crawl around and are susceptible to ingest/inhale higher quantities of smoke dust. It is impossible to control all the environments that your children are exposed to but here are some basic tips to minimize third-hand smoke.
As a smoker, it is difficult to protect children as the dust is transferred via skin and clothes; quitting is the best and healthiest option. However, here are some simple tips to limit the exposure and spreading of third-hand smoke: shower after smoking, wash clothes immediately, do not smoke indoors as ventilation machines are thought to be ineffective.
If your home is exposed to smoke, the dust can remain for months - consider having everything professionally cleaned with non-toxic products.
Similarly, it is best to frequent non-smoking establishments not just sections in restaurants and always opt for non-smoking hotels not just rooms.
Background: On February 8, a study from the Lawrence Berkeley National Laboratory at the University of California was pre-published online in the Proceedings of the National Academy of Sciences (PNAS), research journal, "Formation of carcinogens indoors by surface-mediated reactions of nicotine with nitrous acid, leading to potential third-hand smoke hazards." The researchers found that in addition to second-hand smoke there may be a lingering carcinogenic danger in smoke dust termed third-hand smoke.
Full study, "Formation of carcinogens indoors by surface-mediated reactions of nicotine with nitrous acid, leading to potential thirdhand smoke hazards": http://www.pnas.org/content/early/2010/02/04/0912820107.full.pdf+html?sid=8f61f921-a6c1-453f-8dae-d4cce25d8b6f