How were the layers of the atmosphere discovered?

Answer 1

The first research was done by climbing mountains.
The following research was done by balloon. In fact, the very first balloon launchings with men on board had thermometers and other instruments. People doing high altitude research early died when they misjudged oxygen and cold levels. For much of history, balloons, manned and unmanned, have been able to go higher than planes and stay longer.

Answer 2

probably by launching something into space