Traditionally, St. Patrick's Day was the day to plant potatoes in East Tennessee. However, this year the day falls on Sunday, and none of my ancestors would have approved of tater planting on the Sabbath.
Thus, today would be the perfect day to plant potatoes. They will be ready to dig anywhere from three to four months from now, depending upon the variety you select.
Some good options for East Tennessee are:
Kennebec--A standard white potato with brown skin, Kennebec is a good keeper.
Red Pontiac--Red-skinned, white-fleshed Red Pontiac is good for potato salad.
Yukon Gold--Yellow-fleshed Yukon Gold is an all-purpose potato that keeps well.
All Blue--The name says it all. Blue potatoes are similar to Russet. They make good bakers and fries.
Irish Cobbler--This old heirloom produces both red- and white-skinned potatoes with excellent flavor.
Buy seed potatoes from a garden center. They will have been certified free of potato viruses that can infect your growing beds if you use potatoes from the grocery store. About five pounds of seed potatoes will produce an abundant harvest from a small space. Potatoes are not picky about soil fertility, so long as the soil is deep and contains lots of organic matter. Cut seed potatoes into chunks, each of which should have two to three eyes. Place the chunks, eyes up, in the bottom of a trench dug three inches deep in the garden bed. Space potatoes 12-18 inches apart.
When the shoots are 6 inches tall, pile compost or soil around them so that just the tips are exposed. When another 6 inches of shoots are visible above the soil, hill them up a second time. Then leave them to grow until you are ready to harvest. Potatoes need an inch of water per week, and should have a side dressing of balanced fertilizer after the second hill-up.
When blooms appear on potatoes, you can steal a few new potatoes from the hill by carefully digging in with your fingers. For storage potatoes, wait until the tops have died and shriveled.
I don't consider potatoes an essential garden product. In spring, if you have limited space you are better off growing spinach, lettuce, green onions, radishes, and miscellaneous leafy greens instead of using the space for potatoes. You will harvest many more servings per square foot.