Place the peanuts in a strainer or colander, and rinse under water. Shake off any excess water and drain well. Spread them out in a single layer to air-dry for at least 30 minutes.
In a clean wok or a wide, deep pot, add the air-dried peanuts and enough oil to just cover the peanuts. Then turn on the heat to medium low. Gently and slowly push the peanuts around to heat them evenly and prevent burning. (You must use cold oil and low heat to start, and use low heat throughout the whole frying process. Don't rush the process, or the peanuts will quickly burn.)
As the oil heats up slowly, you will first see small bubbles in the oil, then some steam coming as the moisture in the peanuts cooks off. You may also hear small popping noises (like much quieter popcorn). Keep slowly pushing the peanuts around in the oil. The peanuts should be done once the pink shell on the peanuts turn a shade darker (like a light mahogany brown) and the popping sounds stop. Frying time should be around 7 to 12 minutes, depending on the size of the peanuts.
Because the peanuts burn easily, towards the last 1-2 minutes of cooking time, it’s a good idea to turn off the heat and let peanuts continue to cook in the hot oil without the risk of burning. Strain the peanuts out of the oil. Spread them out in a single layer on a baking sheet or plate to cool them quickly. Another quick cool-down method is to put the peanuts in a large stainless steel bowl and roll them around to disperse the heat quickly, so the peanuts can turn crunchy faster. Toss with salt (this step is optional), and serve!
Notes
Store any leftovers in an airtight container. Be sure to strain the oil and save it. It will have a light peanut flavor and is great for cooking.