First you need to set up a seed starting station with lights and heat mats. I like to use a rack for starting seeds as it allows you to grow more in a small foot print. I have an article on my blog that outlines the equipment I use.
Before starting your pepper seed, you need to decide on what varieties of peppers to grow. But starting seed for all varieties is the same. Hot peppers may be started a little earlier than bell peppers, but that is the only difference.
I prefer to start seeds in plastic 6-packs as they retain moisture better. And then I up pot to Solo cups as they are deeper than traditional 3-4" pots. Be sure to disinfect supplies if re-using them.
Lightly bury the seed and press it down so the seed is in contact with the soil all around. Cover seed lightly, then give each one a good soaking spray of water.
Place the seed tray on a heat mat and cover with a plastic dome to keep the humidity high until the seeds germinate, and place underneath a grow light. Remove the dome once the seeds germinate.
Once your peppers grow their second set of true leaves, it is time to up pot them into larger pots. You can remove the heat mat but keep them close to the lights as they continue to grow.
Be sure to spend a week or so hardening of your pepper seedlings slowly outside, before planting them. I have an article on my blog that teaches you how to do this.
Peppers are a heat loving crop, and cannot be planted outside until night time temps are consistently above 50 degrees. Do not plant on or near your last frost date, check the extended forecast and be sure night time temps will be safe.