Since I don't have a lot of space to play with, I always grow my potatoes in pots - usually one tuber per 10-inch pot. I grow mostly First Earlies, which mature quicker than the other types (about 10 -12 weeks from planting).
When planting potatoes into these pots I only quarter-fill them, using general-purpose compost with an added handful of pelleted chicken manure. I then water the pots, settle the seed potatoes firmly into the moist compost and cover them to a depth of about 3 or 4 inches. As I mentioned, after a couple of weeks (if the weather is decent - more if it isn't), tiny green shoots will appear above ground. When this happens I cover them again with a layer of compost. I do this 2 or 3 times over the next few weeks until the pots are nearly full.
Earthing-up the potatoes like this encourages the production of more tubers along the stem. The tubers form just below the surface - and of course "the surface" moves as the plants grow taller. If you are growing the potatoes in open soil the earthing-up process also gives the plants more stability, prevents light reaching the new tubers (which will make them green), and assists with weed-control.
Potatoes can be planted any time from the end of February onwards, but of course in the UK at that time of year there is still a strong risk of frost, which can be very damaging for tender potato shoots, so I protect mine under a plastic cloche thing (it's officially called a "Seedling Greenhouse" - it's like a Coldframe, taller at the back than at the front). It holds nine of the 10" pots.
Since I only have one of these cloches, subsequent batches of pots don't have the luxury of such upmarket accommodation! The wire grid seen in my photo below is a spare shelf from one of the upright mini-greenhouses. It serves to deter the foxes from nosing about in the pots.
Of course, if frost is expected you need to think about providing some protection from the weather as well as from the local fauna. Here's a couple of ideas. You could put some scrunched-up bubble-wrap or fleece in each pot like this:
|Bubble-wrap (Left) and Fleece (Right)|
Or you could protect a batch of pots collectively, like this:
I think it's worth going to a bit of trouble looking after your potatoes, because home-grown new potatoes are a real treat (especially eaten more-or-less immediately after harvesting) because they have flavour and texture far superior to anything you can buy in a shop.