Before putting in your eggs, heat up the pan and put in some oil/butter. A spatula that can scrape well (flat-nosed, or moderately flexible plastic/silicon) is also helpful.

For a spell some years back, I had a game of "find the worst pan in the kitchen and see if I can cook my eggs without them sticking". Not quite a 100% success rate, but pretty close. (That was mostly scrambled, though. Fried eggs and omelettes are more difficult.)

It's true that a non-stick pan makes it much easier a beginner, but the downside is that said beginner will destroy a non-stick pan within weeks.