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After the last frost date of your region, it's time to repot them into their final container (or bed outside). Just take the whole lump of soil out of the pot, and shake it very lightly to open up the clumped roots and packed soil and plant them as deep as possible, ideally up to the lowest leaves (you can remove those later on if they touch the ground, but you want your plant to be as stable as possible in the ground). Also after every repotting, water thoroughly! This helps setting the soil around the roots.
If you don't plan to put your peppers outside, the right time for this final repotting is when you see roots coming out of the pots' underside.
If your plants are supposed to go outside and they become too big way before the last frost date, you can keep pruning them.
A few additional notes:
If you only want a few pepper plants, don't waste money on a green house, wrapping foil over the pots with a few holes works as well, or use those bubble tea cups with a domed lid, with holes in the dome, as starting pots.
Pots: For final pots, space is key. Some varieties do well in small pots, others hate it. Something bucket size should be the very minimum you should consider. Go bigger if you can.
All, ALL pots need holes in the bottom, you need good drainage, I can not stress this enough, peppers hate to be water logged and they will rot, get stunted or die! Add perlite or something else that promotes good drainage to all your potting soils, starting soils and everything after.
Fertilizing: If you plan to, start a week or two after the first repotting, most general veggie fertilizers work. Fertilize according to the description of the bottle. Some pepper varieties like a little more magnesium than those fertilizers have, just add some coffee grounds to the soil. This will fix it. Also keeps snails away in case your peppers go outside.
Stake your plants, but don't go overboard.
Ask if you have any further questions, /hgm/ is a very helpful.
