I have a few pepper seedlings that sprouted a few weeks ago.
First, to get the seeds, get your hands on whatever pepper you want to grow and let it dry completely on a window sill or something like that. You will know it's dry enough when you can hear the seeds rattle (you might have to drop it on the ground and then pick it up for them to separate from the insides).
A lot of people germinate them first on a damp paper towel, but it didn't work with a couple of my seeds, so I just planted a few others around 1-2cm (never plant them any deeper than that because they do not have much energy stored up for sprouting) in a plastic bottles that were cut in half with holes on the bottom for drainage. I covered them with a little bit of soil and made sure it was loose, or else they wouldn't be able to get through.
After that, I just kept the soil moist (not muddy) and they sprouted in a week (give or take, I didn't really keep track).
This site should help you out;
beginner guide to growing chile peppers
After the roots start showing out of the bottom of your starting pot, transplant them into a bigger pot and be very careful with the roots. Any damage they sustain during this process can stunt their growth (it happened to one of my crops). IMO, this is probably the hardest part.
They like a lot of sunlight (dawn till dusk) and dry weather, so if that's not the case with you and you want to grow outdoors, I would just wait.
Here are a few of pics of my babies;