To get your potatoes to sprout so you can plant them, remove them from the produce-aisle bag, rinse them off, under the tap and then put them back in the clear plastic bag.
Leave them still damp.
Leave the bag on the kitchen counter, for a day and then remove them from the bag. Leave the potatoes somewhere warm and in a few days to a week, they will be growing significant eyes and will be ready to split and plant. :)
To plant them, I take a look at each potato and decide how to halve it so that each half will have as many eyes as possible.
Be ready to plant as quickly as possible since you don't want the cut part to dry out.
Cut the potatoes in half and plant them "eyes up", then bury under a few inches of soil.
To get a lot more potatoes, wait for the plants to grow nice and tall and then put an old tire around them and bury all but the very top of the leaves, in mulch. Every time they grow tall enough, add a tire.
When it comes harvest time, you can pull off the top tire and you will find that the potato plant has grown a ton of potatoes in the mulch, above ground.
They make the best home fries, when you go pick them from the garden, immediately before chopping them up!