Poached eggs seem to have become one of those "you have to do it this way, otherwise..." things - people have their firm opinions on The Right Way. Swirling the water, adding vinegar, etc.
Discovering a love for them decades after learning most of what I know about egg cookery though, I decided to start as simply as possible, then add whichever bits of accepted technique seemed to be needed. And it worked with no need for any such additions. I pour boiling water into a hot, shallow (frying) pan, turn it down to almost nothing so the water's not moving and therefore not likely to disturb the integrity of the not-yet-set egg, and crack an egg into it. And that's it. Timing's difficult as egg freshness is variable, but about 3-ish minutes? When it looks done and responds to a poke with the right amount of set-white-but-obviously-liquid-yolk yield, it's pretty much done. Lift with a slotted spoon or fish-slice, drape with kitchen roll for a few seconds to absorb excess water, and slide onto toast (or whatever).
And that seems to work. No swirling (which risks thrashing the unset white throughout the boiling water), no vinegar (which is too dilute anyway to actually help much with setting the albumen), no plunging into cold water to arrest the cooking process. Just cracking an egg into unmoving water that's hot enough to cook it, and lifting it out when it's cooked.