It would depend on the peppers- but worth a try, I let a pepper mature on the plant, then dry, seeds I keep on a paper towel to help them not rot, and I keep them in a paper envelope with type of pepper and date collected- tho there are many diff ways to do this. Good luck
As kittriana says, it depends on the pepper variety. If you remember the variety name you can Google it to see if it's an Open Pollinated (OP) variety you can save seed from that should come "true to form" vs first Filial (F1 Hybrid) developed from 2 different parent lines, the offspring of which can vary greatly.
When you're ready to germinate the pepper seed you can enhance the process using several methods to ensure quicker, more even germination by breaking down the seed coat enzymes.
All I have ever done is provide bottom heat and make sure the medium stays damp. Older seeds I soak but I don't know if that really helps. They are always slower to germinate then tomato seeds. I've heard of people waiting a month for some to germinate, but I've never waited that long.
If you're going to save seed, know that unlike tomatoes, peppers cross-pollinate readily with any nearby peppers. So unless all the plants growing near one another are all of the same variety, you might want to consider using pollination bags to eliminate the possibility of cross-pollination by insect visitors.