As you know, soaps dry your skin. Any kind of detergent is going to clean your face by stripping all of the oil away. But for most of us - particularly in winter - you may end up having to replace that oil with moisturizer.
There are two reasons why this is a bad thing. First of all, it's much less damaging to your skin if you can avoid stripping it in the first place. Second of all, moisturizers are often mostly useless at best; toxic at worst. They can contain artificial pigments and scents which may be toxic (it's hard to say, since cosmetics are not regulated by the FDA), as well as parabens which are known carcinogens.
And it's all a lot more expensive than what you need to use the Oil Cleansing Method! I know a lot of people who have followed the OCM for years and rave about how great their skin looks. They get compliments from strangers! (When was the last time you saw a grown adult get a compliment on their skin from a stranger? CRAZY.)
A lot of people equate oily skin with acne. But oil on your skin doesn't cause acne. Acne is caused by bacteria, which feed on trapped "stuff" inside your pores. When your pores get clogged with dirt and skin flakes, the bacteria go nuts and soon you have a blemish.
To the contrary, your skin NEEDS oil. By applying moisturizer to dry skin, you're just re-oiling your face. Moisturizer manufacturers tout terms like "moisture" and "quench," but your skin doesn't need water. When your skin says "I need moisture," what it means is "oil."
That being said, your skin also needs to be cleaned. The challenge, then, is to clean the dirty oil off your face, remove the blockages from your pores, and also leave behind a clean oil. Sort of like giving your car an oil change!
The basics of the method are simple. Massage a bit of oil into your face, use heat to steam your skin and open up the pores, then wipe the excess oil away. The specifics are almost infinitely variable. Most articles I've read have you use castor oil as a base, with a bit of another oil to help lighten it up. This article, for example, has you start with a 50/50 blend of castor oil and extra-virgin olive oil.
As for the steaming portion of your daily facial, most people seem to use washcloths. Run it under some warm-to-hot water, wring it out, drape it over your face, and chill for a few minutes. (This method apparently generates a lot of super-oily washcloths, so you might want to rinse them with dishwashing liquid after you're done, but before they go in the laundry.)
Now all I have to do is find a place to buy castor oil locally, and I'm totally going to give this a try!