I loosened the nut that you can see in the picture and took it right off. I thought the pedal crank would fall right off. It didn't.

Under that nut is the end of a screw. I thought I could just unscrew it from the other side of the crank, but it has a circular head.

I didn't want to muscle it, so I thought i'd ask on here.

Thanks in advance.

Looks like on old cottered crank - you might want to have a read through this.

This is a "cottered" crank and the nut just retains the cotter pin which, typically, has to be driven out with some force. Done properly the cotter is removed with a purpose built or improvised press. It can also be hammered out if the crank arm is supported well. Do a search for "cotter crank removal" as there have been numerous thread on the care and feeding of this type of crank.

I just had a go. It didn't end well.

I didn't have a vice, or another piece of wood so I just rested the pedal against a concrete step. I then unscrewed the nut a few turns and got an old chisel that I turned the other way around to knock it out. I sprayed WD40 into the hole, and left it 15 minutes.

When I tried whacking it, nothing happened. I hit it really hard a few times but it still wouldn't budge. I then checked to see if there was any damage, and i'd slightly damaged the thread on the nut and the cottered pin.

I decided that was enough and was (luckily) able to put the nut on. I just wanted to take it off to grease my bottom bracket, but I don't think i'll bother now. I'll ride on it until it starts making funny noises, and then swap it for a cotterless one.

Cotters are tricky. When I use improvised tools to get one out, you usually have one or two chances before you damage the threads. What that means is that I support the crank arm itself on an extremely solid surface like a solid piece of pipe that fits around the cotter and a concrete ground. Then I loosen the nut up about 2 turns and hit it as hard as I can with a heavy 5 pound hammer directly on the nut once or twice and that usually knocks it free. If you baby it by hitting it with a small hammer not very hard and/or don't have the crankarm supported extremely well, then the shock you are sending to the cotter won't break it free but rather will be absorbed and the threads will still become damaged.

A 15 minute soak with WD-40 is next to useless!
Get some REAL penetrating oil.
Apply multiple times for a couple days.

I use a 4" machinist C clamp (fine threads)
Back the nut off so that it is just flush with the ends of the threads.
Use a small socket for a "receiver" on the unthreaded end.
Keeping the clamp aligned, tighten it down TIGHT.
If it doesn't immediately push the pin, let it sit for an hour or 2.
Try tightening again.
During your 2 day "pre soak" occasionally "ring" the area with a SMALL hammer or similar to encourage the PO to wick in.

I would NEVER encourage somebody with limited experience to use a Big Hammer on these unless you plan on replacing everything, including cranks, cups & spindle.