All you need is to
a) hook up a hose to your sink spout
b) run the hose to the floor where you pass it through the jaws of a strong spring clamp
c) run the hose back up to the sink head (or wherever you wan to send the water)
the most annoying part is adapting a hose to your sink spout. If done incorrectly water will leak out at the junction. As long as the leak isn't much you're still conserving water but try to make the adapter as tight a fit as possible. The tips of many sink spouts unscrew, so you could maybe but a properly threaded adapter somewhere but I just used hot glue (see the glue gun in the video) and the cap of a contact lens cleaner to make a pretty good adapter.
Here are some supplies that you could use to build the system in a reliable non-leak way:
1) short garden hose with rubber gasket (get two) (see: http://www.amazon.com/American-Specialty-UT-10-Multi-Purpose-Utility/dp/B000T2B468/ref=sr_1_14?ie=UTF8&qid=1378139332&sr=8-14&keywords=Short+Garden+Hose)
2) Garden hose-to-sink adapter (as described here: http://www.wikihow.com/Attach-a-Garden-Hose-to-a-Kitchen-Faucet)
3) Garden hose foot pedal (as shown here: http://www.amazon.com/Nelson-Yardworks-Water-Pedal-Control/dp/B002URLTXS)
best of luck!