The way I do it is probably pretty terrible but it consistently works for me (moist chicken but well browned).

1. Take chicken breast, or something of similar thickness, dry, and season. If I'm doing this way it's because I'm lazy or lacking in time or don't have things prepped (and I want to make something else while the chicken is cooking) so I don't brine.

2. Heat pan (on 5/10 on my electric stove with a decent non-stick pan, or slightly lower if my stainless all-clad) till pretty hot, add regular olive oil, then add the chicken. Cover.

3. The lid is going to help cook through, but, you can't keep it on because water will accumulate and limit your browning. So about 1/3 or 1/2 of the way through I will take the lid off. You could also probably just keep it on but cracked (the entire time).

4. Flip when about half done. The bottom should be nicely browned. Turn up the heat a notch or two. Again, the lid comes off at this point if not before. Sometimes I'll even drain a bit of water if its too excessive, or move the chicken to a drier spot in the pan.

5. Take off heat just a bit before usual. It'll cook through. Never ever overcook chicken!

Note this will take longer to cook than other methods.

The (possibly wrong) theory behind this is that initially the pan is more than hot enough to brown the chicken one one side, even with non-smoking olive oil. When you add the chicken, the pan will cool, and will soon be back to "5", but not before browning occurs on one side.

The lid will help cook through but you need to make sure water doesn't accumulate, as this will steam the chicken instead of browning (same reason you dry the chicken). The lid is important because a thicker cut of chicken will take longer to cook through, which will also brown (or more likely burn) the chicken, but it will dry out the outside too much if you didn't use a cover for part of it.

Then the temp kick at the end is to promote browning on the other side, since the pan is cooler than when you started, and there's likely more moisture as well, so you want to get rid of that ASAP.

Of course, if you have a thinner cut, that's easier, because you can just not use the lid, increase the heat (6ish or 7... again, this will vary by pan and stove), and use a higher heat oil (grapeseed, sunflower, clarified butter, etc). You'll cook through about the same time as browning is complete and won't have to fuss with it so much.

Another option I like is to just sous vide the chicken until proper temp (my preference is 144F), dry it, and put that baby on a blazing hot pan with a high heat oil, for about 30 seconds a side. That is about as fool-proof and easy as it gets, though it'll take 1-2 hours for the chicken to cook.

Last but not least, you can always sear the chicken on high heat and then stick it in the over to cook through.