When do carp start moving into the shallows? Is this dependent on water temp, or the amount of daylight?

I catch carp in the shallows all during the year. However, January and February are the hardest months to find them in the shallows. I would go with temperature over daylight as a controlling factor. All I know for sure is that they are active right now.

Both. Carp will be in the shallows year round. In Spring they seek shallow vegetation to spawn. In Winter on a warm day they'll bask in the sunlight in shallow water. Year round they'll come shallower at night to feed.

And how do you catch them? Such as what kind of rod and whether a float should be used. I hear that corn and white bread is a simple way of catching them.

On all of the lakes I've been on in the last few weeks, they've been spawning right next to the bank.

Kids and I love to carp fish. We use a simple Carolina rig with a small hook. Corn is our bait of choice. I recently bought a big bag of range cubes so typically we will throw those out, then go back up to the truck and grab our gear then start fishing. If you can get out days before to bait up an area, that's even better. I just don't typically have the time as most carping holes we hit are 45 min away.

If I use a rod and reel, then I fish with range cubes after chumming with them. Here is how I rig them: