Back in September I was lucky enough to receive a black Oca tuber brought from Lima. It was determined to sprout, having just been whisked away from Peruvian springtime, and despite being stashed in dry sand at low temperature to try to hold it through the winter, the tuber took a while to get the idea, and in the mean time produced several long shoots. Although unintended, once the situation arose, the propagation opportunity was just too good to miss.
'Slips' can be taken in a similar way as with sweet potatoes.
Roots start to develop from the Oca tuber itself, but what makes this method so easy is that roots also tend to form spontaneously at the base of the shoots if they are in contact with soil. It's a simple matter to gently break away the shoot, roots and all, and install it in some sandy compost.
Add gentle warmth, and after a couple of weeks the plants are growing away.
It's an easy way to multiply up a particular cultivar before the start of the growing season.
Placing the tuber in just-damp sand with some warmth during late winter should encourage the rooted shoots to appear.
Incidentally, cuttings taken from growing stems are also very easy and reliable. A large cutting taken as late as September will even be able to form a few small tubers before the frost arrives.
To give an idea of Oca's vegetative powers, I've seen diseased stems that have been completely rotted through near their base (photo here), collapse on to the soil, put down new roots and recover unaided to form a new plant. So no need for hormone rooting compound here!