What causes an electron in an atom to move to a higher energy level?
An electron will jump to a higher energy level when excited by an external energy gain such as a large heat increase or the presence of an electrical field, or collision with another electron.
Electrons can gain energy from outside sources that may be intense enough to allow them to jump from their present levels to their next higher energy levels. Excited electrons in higher energy levels do not stay there long, as they prefer to return to their normal levels.
Rapid oxidation (or burning) of many elements will result in colorful displays. Electrons excited into higher orbits by the heat of burning will jump back to their original orbits as the material subsequently cools, giving off energy photons in the process. This can be seen in the flames of fires, and the spectacles of fireworks.
When an electric field is passed through an element in the gaseous state, is electrons will jump back and forth between higher and lower energy levels to emit certain frequencies of photons specific to the element.
Collisions between atoms can also result in electron energy jumps, but viewing these results is not as common.
There is information about energy levels here:
Calculations of energy levels can be found here: http://skyserver.sdss.org/dr1/en/proj/advanced/spectraltypes/energylevels.asp