How Do You Recycle Oil?

Your options depend on where you live.  

Some countries and some local authorities have facilities for recycling machine or engine oil.  You need to phone your local authority with responsibilities for waste disposal to find out whether any such opportunity exists in your area.  They can advise, otherwise, how to dispose of waste engine oil.

I didn't know if maybe you meant cooking oil.  Technically, this shouldn't go down your drains (clogs them).  Until a few years ago it was possible in some places (Belgium, for instance) for ordinary members of the public to take used cooking (vegetable) oil to depots for recycling.  There it would be made, typically, into other food products or livestock feed.  Unfortunately, some got contaminated and got into the human food chain.  Big scandal.

Cooking oil can also be made useful into bio-diesel, but a person needs specialist equipment to do this.  Some car engines have even been modified to run straight on vegetable oil (it's just poured into the tank, and the car has it's own conversion equipment inside).  You could ask in your local area if anybody is collecting old cooking oil for this purpose.