You can pour cooking oil down the sink, but it's not a good idea. Cooking oil poured in the kitchen sink or flushed down the toilet causes a variety of problems.
As cooking oil cools and solidifies, it will clog drains and pipes, either in the home or in the community sewer system. Cooking oils are not toxic, but they can still harm the environment by coating plants and wildlife.
Always allow oil to cool before disposal. The easiest way to do this is with an old-fashioned grease can. Keep a coffee can near the stove. When you're finished cooking, pour the used oil into the can instead of down the sink. When the can starts to fill up, put the lid on the can and discard.
Oil can be put in the trash if it's not a large quantity. One coffee can probably won't be a problem. If you have a lot of oil from an appliance like a turkey fryer, it would be better to take it to a local oil recycler. Another possibility is finding someone who uses oil for biodiesel.