Rinse the oil-based cleanser off your face with warm -- but not hot -- water. If your water is too hot, it can dry out and irritate your skin.
Wash your face again, this time with a cleanser formulated for your skin type. A general rule of thumb: Dry and sensitive skin types fare best with creamy cleansers. Those with oily skin should look for a cleanser that balances oil levels without stripping skin of essential moisture, like a gentle foaming cleanser.