The Oil Cleansing Method is a way of washing your face, but using oils instead of soap. It sounds counter intuitive, but if you remember back to the like-dissolves-like principal from chemistry, it makes a bit more sense.
This was what I originally pinned, and it has a more in depth explanation about the various oils you can use. I started with a basic mix of 1/3 Castor Oil to 2/3 Olive Oil. I've been using this for about 5 or 6 days and so far I really like it. My skin feels soft after, and I haven't been using moisturizer. The Castor oil can be drying, while the olive oil is more moisturizing, so you may need to tweak your formula depending on your skin type.