I haven't grown potatoes myself, but I'm linking to an article that compares several common methods. Good luck!

Here is a link that might be useful: 7 Ways to Plant Potatoes

You already mentioned most of it.

If your seed potatoes are about the size an extra large egg, no need to cut. Plant about two per hill(about 3" apart, about 4" deep. The next hill should be 12 to 14" away. In other words, hill spacing is 12" to 14".But if they are bigger , cut them in half, such that each has 2 to 3 eyes.

If you plant more than one row(several hills in a row), the next row should be 2 to 3 ft apart. Professional farmers leave more space because the rows because they plant, cultivate and harvest with machines. If you have plenty of garden space, place them 3 ft apart . But I can do with much less than that; i.e. just enough space to walk and work between the rows..

Now that you arranged your hills and rows and planted your seeds, Depending on soil condition you may dress the top of hills with manure, all purpose fertilizer, Needless to say that you could have amended the whole bed with compost, manures etc before planting too.

Now that you planted the seeds, wait till they sprout. When the sprout are about 8" tall(+ or - an inch) start HILLing. It means filling around the stems with some nice fluffy soil. This s the medium in which future tubers will grow. You may repeat this(hilling) one or twice later , when the stems are again sticking out 8_10". But after that just leave them alone. Water them regularly and fertilize once or twice. The purpose of hilling is bobble or triple folded: to provide enough under soil stem length, on which tubers should grow. It is also a medium for tubers. And lastly, it keeps the root system cooler and moist longer.

Yeah a couple of questions about seed potatoes regarding that you put. Do you have to actually cover the seed potato with soil when you plant them, or should the sprouts on the seed potato be exposed? Do you partly cover the potato and just leave the sprouts showing when you plant seed potato?

Also you said when they're 8" tall you cover the shoots. How many inches of soil do you cover the seed potato with when you initially plant them?

When the seed potato is the height you mentioned, do you fully cover the seed potato or do you leave it exposed?

All your follow up questions are answered in detail in the article Brittany linked for you above. It even includes how-to pictures.

You can also find all the answers in the previous discussions here about how to plant and grow potatoes that the search will pull up for you.

Dave

kawalinko;

I already said to cover the seed by 3 to 4 inches of soil. IN OTHER WORDS plant it 3 to 4 inches deep, Under the seeds there should be good soil too b/c the roots will grow downward and sideway. For example, if you plant them in raised bed of 12 inch high. Then dig a hole 6" to 7" deep, place seeds, cover 3". In effect the seeds are in a hole. later on when they shoot, you fill up that hole and build hill around it even higher.

ABOUT THE EXISTING SPROUTS: again no matter there is a sprout on the seed or not, has to be covered by about 3" of soil. If, just in cast sprouts are longer than 3 to 4", then cover the sticking part with hey/straw/peat moss...etc.