How do you poach chicken?
By hunting chicken in a game preserve? ;-)
The essence of poaching chicken is a gentle boil in water, stock or other flavorful liquid. I really like poaching chunks of chicken in a thin sweet-and-sour sauce, then thickening the sauce, adding pineapple chunks, and serving over rice.
Others have mentioned the technical definition (cook in simmering water), but well, I don't do that.
First, I've never tried poaching a whole chicken, only pieces. And I'm not sure you'd want to poach a whole chicken, so you'll likely want to cut it into pieces first.
If I'm poaching, it's typically because chicken was on sale in bulk packs, so I'll buy a few pounds, poach it, shred it, and freeze it for later usage ... so I'm doing a few pounds of chicken bits at a time.
I use a large pot (doesn't have to be a stock pot), and fill about 1/3 to 1/2 way with water, add a bit of salt, and bring it to a boil.
I add the chicken parts, bring it back to a boil, and then turn the heat to the lowest setting, and leave it with a lid on for an hour.
The boiling helps to kill any surface bacteria that you might not achieve by starting the chicken in cold or simmering water.
If I'm planning on saving the poaching liquid too, I'll add a few bruised cloves of garlic, a sliced up onion or two, some carrots, and whatever other sad-but-not-yet-spoiled vegetation I might have in my fridge (or moved to the freezer specifically for this purpose). Once I've shreded the meat, I'll add the bones back in, turn the heat back up, and let it simmer for a while, then strain it and freeze it. Depending on how much storage space I have (and if it's winter or summer), I might cook it down to concentrate it, but I've learned that forgetting about it and burning bones is really, really bad (it stinks, stains even stainless steel pots, etc.).
To poach anything you heat a liquid to just under a simmer and place your whatever into the liquid until it is cooked. The trick to poaching is using a flavorful liquid (although you can use water if you don't want to add any flavor to the dish). Chicken specifically should take about twenty minutes for a boneless breast, longer for chicken with a bone in it. Check your chicken with a quick read themometer before removing to make sure you crossed the 165°F (74 °C) degree mark. Make sure you have enough liquid to cover the chicken.
The process of poaching chicken simply involves cooking chicken fully submerged in a liquid until done. You could do this with just water, but it'll taste quite bland. The liquid should be hot but below the boiling point; shoot for 190 F (88 C).
I suggest using low-sodium chicken broth, or a combination of low-sodium chicken broth & water as a liquid though. Why low sodium? So you can add salt to taste.
You can also jazz it up a bit by adding some chopped vegetables to the liquid. e.g. carrots, celery, and onions. If you do this, bring it to a boil first, then reduce heat to the aforementioned range.
As with any cooked meat, use a thermometer to determine doneness - 165 F (74 C). The cooking time can range widely (from 15 to 45 minutes) depending on the size of the pieces. Yes, you can even poach a whole bird.