Avoid getting grease in your drain. It is not a good idea to pour any kind of oil, grease or fat into your garbage disposal. The grease can accumulate in the disposal unit, slowing down the motor and lining the pipes, causing the drain to clog. Try to wipe off as much grease as possible from pans and roasting tins using paper towel, before rinsing.
Some other kinds of garbage disposal units are powered by water pressure, rather than electricity. Instead of the turntable and grind ring described above, this alternative design has a water-powered unit with an oscillating piston with blades attached to chop the waste into fine pieces. Because of this cutting action, they can handle fibrous waste. Water-powered units take longer than electric ones for a given amount of waste and need fairly high water pressure to function properly.
Plug the disposal and fill up the sink with hot water and detergent. Unplug and run the disposal. The spinning disk forces the water down the drain like a pump. This should clear the disposal and the drain line. If not, you'll need to inspect the plumbing. Old pipes made of iron clog easily due to internal corrosion and should be replaced with copper.
But to dislodge whatever’s causing it to be in a bind you can use the hex wrench that came with the garbage disposal. I know most people lose them, that’s okay. Grab your set of Allen wrenches, get the right size, insert it into the recess hole right in the bottom of the disposal, and turn it left and right until you dislodge whatever caused it to get into a bind.