How do the properties of the atmosphere change with altitude?
Pressure and temperature drop up to a point, up until the point where the temperature increases.
This topic could take up several chapters in a text book so I will just give you the highlights.
Pressure drops with altitude. Since pressure is directly related to how much atmosphere you have over you, the higher you go up the less atmosphere you have over you and the pressure drops.
Temperature drops with altitude up to a point. As pressure drops so does temperature, this relationship is seen in the Gay-Lussac's law. However, once you reach the Tropopause (layer between the Troposphere and Stratosphere) the temperature stops decreasing because of the ozone layer. The ozone layer blocks the majority of UV light energy that comes to the Earth from the sun. As a result that ozone is going to heat up, and this balances out the temperature drop from lowering pressure.
As you rise up in the Stratosphere, the pressure drops until you get to the point that it is almost zero. At that point the atoms and molecules of air are quite far apart (often going great distances without interacting with each other).
Above the Stratosphere temperatures keep dropping in the Mesosphere. The reason for the temperature dropping here are not well understood, since it obviously has little to do with the pressure since it is essentially zero through the whole layer. Since the atmosphere is primarily heated from the heated Earth at these altitudes that heat does not reach it. The top of the mesosphere is the coldest part of the atmosphere.
Above the Mesosphere is the Thermosphere, where the atmosphere loses any uniformity. It is just individual particles that start becoming super heated by the energy of the sun. At this point the particles are so far apart they rarely interact. The temperature of individual particles will reach over 2000 degrees but since the particles are so far apart temperature doesn't mean anything.