To grow a hedgehog, ball, or barrel cactus (Echinocereus, Coryphantha, Pediocactus, etc.), you first find a place where it will grow, and plant it there. The place should have sun for most of the day, without shade. If this spot is AGAINST A SOUTH-FACING WALL, THIS IS IDEAL. The soil should dry out often, and never stay moist for long. It's great if nothing else grows there already, since cacti don't compete very well with other plants and weeds.
If you don't have a good dry place in the sun, take a wet place in the sun, and make a raised bed there. That is, pile up the soil there, or make a box about 12 inches (30cm) above the wet ground, and fill it up with very sandy soil. Don't mix in any compost. It looks nice to add large, flat rocks on top of the soil.
IT IS VERY IMPORTANT to keep the soil very dry during the colder months (October through April here in Southeast Michigan), and not very moist the rest of the year. During those cold months, and during wet weather the rest of the year, shield the plants with a window of 1/4 inch thickness shatter-resistant Plexiglass� or similar material, leaning against the wall, or build a device to hold it there. You will have to watch the weather forecasts to do this. A little rain now and then will not hurt them in the summer and spring, but in a very wet summer, you can easily loose many of your plants. They also don't need any water in the winter, and it can kill some plants to be wet in the winter.
Never make an enclosed box or mini-greenhouse around your plants, unless you know what you're doing (and I don't, with greenhouses). YOU DON'T NEED TO KEEP THE PLANTS WARM, just dry. Wind will never hurt them, and neither will ants, unless they bury the plants. Ants also carry off and eat the seeds, so if you're saving seeds, watch very carefully to get them before the ants do. Even the ants here in Michigan know what to do with cactus seeds, which they probably haven't seen in thousands of years.
Where do you get the plants? Well, the best way is to buy them our take cuttings from another plant. You can cut it from the plant with a knife. Cut the stem at a narrow spot, or at a stem joint. Let the cut surface dry out for at least three days, or better for a week, so it can make itself immune to fungi. Then it's ready to root. You will need no rooting hormones, so just place the piece where you want it, ON THE SURFACE, NOT INTO THE SOIL. It might root by itself. These are not as easy as the Opuntias.
You can also grow them from seeds. I don't use all the methods which tell you to plant them in a closed atmosphere. I fill a pot with coarse sand, put the seeds on top, and then put a very fine gravel over them. Do this in May or June, when the temperatures are above freezing but not a heat wave. Water them with a very gentle sprinkling of water, but soak the pots when you water them. Water them every other day if there is no rain. Put the pots out in the full sun, and the seedlings will quickly adapt to it.
As soon as the seedlings are large enough for you to handle without crushing them in your fingers, plant them in place. Plant them between two larger rocks, to hold a little moisture. Water them with a dropper, and water them a lot, every few days. If the plant is really green, then protect it from sun by putting a rock across the two rocks around the plant, so you shade it. I'm talking about plants here which are about 1/8 inch tall or less. They really are amazing. In a few years, they should be about one or two inches tall, and begin to flower.
Whichever type it is, let the plant grow the way it wants to, and don't try to correct the way it grows. The plants always will correct themselves again. If the stem begins to lean over, leave it alone. That means that the plant will branch out at the bottom, like the picture on the top of my homepage. If they want to branch out, let them. It's just natural that way. You won't get a tall single-stemmed cylindrical cactus in a very cold climate (let me know if you do).
Never grow the plants indoors, because the deep shade in any house will stunt their growth, and make the plants too skinny, and they will be too sensitive to sunburn once they finally go outdoors. The best growth comes from sunshine, rain, and free root run. If you have a plant indoors, gradually get it used to the sun, and then plant it outdoors. If the growth is bad from growing indoors, the plant may grow slowly, and then look very strange. You will get thick, stocky, spiny growth on top of tall, skinny, thin-spined growth. Just let it do this, our take a cutting, and the new plant will get a lot bigger and look a lot better than the mother plant.