I can't help ya with corolla specific, I've only serviced my commodore, but should be similar. The nut you have to undo is the sump plug. If you get the front of the car on jack stands or ramps, and slide underneath, you will see it on the engine sump (the bottom of the motor).
What ya wanna do is warm the car up, take it for a drive around the block or something. Get it up on the stands, take the oil cap off, chuck ur pan underneath the sump plug then undo it with a ring spanner (this is so you don't round off the nut). Leave it for 10min to an hour, depending how thorough ya wanna be for the oil to drain out. Remove the old oil filter with a removal tool. Get the new filter, smear a bit of oil on the rubber seal on the filter then screw it on hand tight (don't use the tool to tighten it or you'll struggle to get it off again) Replace the sump plug, it's also a good idea to replace the sump plug washer aswell. Fill with the required amount of oil according to ur manual, replace the oil cap. (Also a good idea to check the dipstick on a level surface, just to make sure) Then take it for a runaround the block, check the sump plug and oil filter for leaks, tighten if necessary and ur done :)
Found a photo of the corolla engine sump, where the yellow paint is in this pic, you can see the oil draining out. It's removed in this photo, but this is where the sump plug will be.
This is what the sump plug and washer will look like, or very similar...