The Kitchn suggests mixing a paste of baking soda and water and coating all the gunk-encrusted surfaces of your oven, then leaving that overnight for about 12 hours. Then you wipe and scrape as much of the stuff off as you can, and follow it up with a vinegar spritz that will foam and help loosen the remaining debris. Cleverly’s method is a little different: You take an oven-safe bowl and dump in some baking soda and water. Then you slowly add some vinegar in, being careful not to have a volcanic reaction on your hands (or all over your counters). You spread this over the inside of the oven. Then you put the bowl and the remaining mixture in the oven and turn it on to 212 degrees Fahrenheit (100 degrees Celsius). Leave the bowl in there for 45 minutes, and you should be able to wipe away the grease with just a sponge, no scraping or excessive rubbing needed.
The video is a little light on the details. Should you wait until the oven cools before wiping it down? How much of each ingredient do you need to make the paste? Well, if your oven is a disaster, you can always channel your inner middle-school mad scientist and experiment.