The Red Tarns Track climbs 300m behind Mt Cook Village on a steep but well maintained track. The trip takes about two hours return. The tarns are sometimes dry, but in December 2013 they were showing their red colour from the pond weed that grows in them. The panoramic view includes Aoraki Mt Cook (reflected in the tarn) and The Footstool (on the left).
Here is a map of the Mt Cook Region (including the Red Tarns Track) that I have copied from the NZ Frenzy website. There is further information about the Mt Cook Region at the NZ Frenzy website.