Hi Jarad,
First you want to plant potatoes the size of a hens egg with one or two eyes. Some small potatoes can be planted whole, if not cut them up. Let them dry a few days before planting. Some dust with a fungicide. Potatoes like a slightly acid soil.
I'm zone 5a so I plant towards the end of April when the last freeze is over. If the ground can be worked it's ready.
I plant 4'' deep and 3' apart. As the potato grows, pull the dirt up around it to keep any potatoes that might try to grow thru the dirt, covered. If they do they will turn green and it can make you sick. We water in dry weather by making shallow trenches around the plants and flooding the trenches.
When they die back they are ready to dig
When you dig, stay a good foot away from the plant, use a fork and go deep. Lift it up and start looking for potatoes that might have fallen off the plant. Gently wash them and dry them in the dark. I put ours in the garage on newspaper with newspaper covering them. We turn them every few days.
For two people a good 2# is enough for us to eat and try to keep over the winter. I don't have a basement or root cellar.