Short answer
Crack a fresh egg into a cup, slide it into barely simmering water and cook for about 3–4 minutes. Calm water and a fresh egg matter more than elaborate tricks.
Control the water
Use a wide pan with enough water to surround the egg. Look for small bubbles rather than a rolling boil. Vigorous movement pulls the looser white away from the yolk and produces ragged strands.
Freshness changes the shape
Fresh egg white contains a larger proportion of thick albumen, so it stays close to the yolk. Older eggs are still usable, but their thinner white spreads more. Straining away only the very loose white can give a neater result.
Vinegar and whirlpools
A little vinegar can encourage the surface white to set, but too much affects flavour. A whirlpool can help one egg wrap around itself, yet becomes awkward for several eggs. Neither replaces gentle heat or sensible timing.