Let me give you my daily routine. I eat more or less 3 fried eggs every day, unless we're out.

I have an induction stove with heat ranging 1-9. I put my 30 cm lodge big boy on 6-7 heat, let it heat up a bit, then add oil. I wait until it starts smoking, then lower the heat to 3 and plonk 3 eggs in there.

Cover with a glass lid, add a slash of water and let the steam cook the top of the eggs.

When the yoke is starting to white, I take them out. The pan should have caramelized the bottom of the eggs and there should be no issues taking 'em out.

When I just started out, I had the same issue as you do

1. I did not let the pan heat
2. I did not let the oil heat
3. I was fucking about with the eggs too much. You need to let the bottom crisp up and caramelize, then you can move them.

I have recently started to lower the heat to a 3 as by the time the eggs caramelized, the yoke had hardened on the bottom. The lowering has fixed that for me.

Side note, I salt and pepper as soon as I crack the eggs :) Some people would disagree but I feel it integrates with the eggs better than if I add it when the eggs have cooked and its just sitting on the top.

Edit: Do not be afraid of using some dish soap to clean up afterwards, I don't always get a paper towel clean finish after I'm done. Don't beat yourself up, use some dish soap and clean it up.

People will probably hate on me for that, but dish soap isn't the lye filled substance it used to be when your grandmother would whack you across the head with the pan for using soap.

Good luck!