Short(ish) version: Leave some beer behind in the fermenter after racking, and swirl up the slurry and save some in a sanitized container. Simply store the yeast under the beer it made. Store very loosely covered (with foil, or a lid not tightened down -- it will probably still be producing some gas!) at, ideally, 34°-37°F. Do not rinse the yeast with water or store in water; old sources may have advised doing so, but these practices are now known to be quite harmful to yeast and to invite infection. Storage life is strain dependent and dependent on storage conditions. Most strains can be repitched directly for up to two weeks, some even longer; if in doubt of the vitality of the culture, you can make a new starter from it to be sure. (Note that your harvested yeast, even if you keep it a while, is usually still much fresher than the new stuff you buy at the LHBS.) For longer storage, you can periodically add wort on top of the slurry to feed it, or just plan to propagate it back up when needed. If the yeast looks odd, smells odd, or the supernatant beer develops off flavors or aromas, you probably want to avoid repitching the yeast. (If you search this forum for this and related topics, your head will soon be spinning and you will be desperately trying to claw your way out of the rabbit hole...)
[EDIT to correct erroneous substitution of "beer" for "yeast" in 2nd sentence. No real change.]