How can you properly use a meat thermometer?

An example- cooking chicken breastfeeding. The meat thermometer claims that the temperature has to achieve 77 degrees Celsius. I cooked it for a brief while at a griddle pan and then set the pan in the oven.

The temperature wrapped around 71 degrees and if it did not appear to be receiving any greater and I believed it was overcooking I pulled it out. Sure , overcooked!