Mixing at home can be great, but time consuming, and your blend may not always be accurate. Thus I'd recommend going with a cleansing oil that comes nicely pre-packaged for you. I like LORAC Oil Makeup Remover and the Shu Uemura Cleansing Oils. With both of these you start massaging the oil into the skin with your fingers(I can use the LORAC one on my eyes too, but Shu's stings a little on the eyes so I use a seperate eye makeup remover) while the skin is still dry. After massaging for a few seconds, dampen your hands with a little bit of water and massage again. Then use a wet wash cloth to wipe it all off. Follow with an alcohol free toning lotion to remove any left over oil and to restore your skins PH balance.
The great thing about cleansing oils is that they are so effective at breaking down any kind of makeup, even thick theatrical cake makeup. Just like with your dish soap (you'll notice the most effective ones on grease contain orange oil), a lighter weight oil breaks down a heavier weight oil. They work on all skin types and never over dry the surface of the skin!