Depending on where you live will depend on what time of the seasons you plant. Some places you can plant twice a year.
I live in a temperate zone with late /early summer frosts so I need to ensure leaves don't appear while in this period. The method I use is to dig a trench 8" deep with a long handle shovel and manure the bottom of the trench with compost or blood and bone fertiliser. The potatoes I use, I don't both cutting in half to plant but use the whole tuber. You can buy certified potato tubers from nurseries or agricultural suppliers. This may ensure you have disease free crop but it isn't 100% from my own experience. This year I chose to plant healthy looking potatoes from the super market.A risk I know but my disease situation couldn't be any worse than what I already have on my property.
These tubers are placed at the bottom of the trench 1 foot apart and backfilled with the soil. As the leaves appear, I cover them with straw with the tops sticking out. This is done several times with the straw maybe as much as a foot deep. When my frost danger is over I allow the plant to go for it without any more mulching.You can just hill up with soil but the mulch is a soil conditioner and the earth worms love it.

A second and a third row are spaced 2 foot and 4 foot from the first.
When the plants go brown and die back you can harvest from beneath the mulch.
I live in the southern hemisphere and plant potatoes here in October. Potato growers in frost free areas plant in August and again in December. It's important to rotate your potato crop to different areas.