Virtually everything we  know about the sky was learned from light from celestial sources. We should first understand the nature of light itself. It is the carrier of electromagnetic energy, and can be viewed equally validly as a wave or as a stream of particles (called photons). In many experiments it acts wavelike: it produces interference patterns, gets refracted (bent) by materials like glass, has a measurable wavelength (l) which decreases as the energy of the light increases, etc. In other experiments it acts like a particle: for example one can build "photon counting" detectors which record individual very discrete arrivals of photons at low light levels. The truth is that in the quantum world, things happen which have no real analog in human experience, and cannot be explained by analogy with our experience.

Photons come in all energies, which means at all wavelengths. Visible light comprises a very narrow range in the full electromagnetic spectrum. Red light has approximately twice the wavelength of blue light, from 350nm to 700nm (nm is nanometers, a billionth of a meter). Longer wavelength light has less energy: they are inversely proportional. Longer than red we have infrared (which we experience as heat), then microwave, then radio wavelengths. Since we cannot see these, we must build special detectors to sense them. Shorter than blue wavelengths we have ultraviolet, X-rays, and gamma rays. These are increasingly energetic photons, and dangerous to life. Luckily our atmosphere protects us from celestial high energy photons, but this means astronomers need spacecraft to make observations at those wavelengths. Certain wavelengths in the infrared, microwave, and long wavelength radio spectral regions are also blocked.

In principle, objects at any temperature produce all wavelengths of light, but in practice the light they produce is mostly near some peak wavelength, which depends on temperature. Wein's Law expresses this relationship: l_peak(nm) = 3x10⁶ / T(K). So humans, with a temperture of about 300K, emit primarily at 10⁴ nm (also called 10 microns; a micron is a millionth of a meter) which is in the infrared. Any body which is opaque will produce a peaked spectrum of photons, called a "blackbody" spectrum (because a perfect emitter is also a perfect absorber and would look black). For a given surface area, a hotter blackbody will emit more energy at all wavelengths, with a peak at shorter wavelengths. The total energy emitted depends on T⁴.
Not everything emits like a blackbody.

Atoms consist of nuclei surrounded by electrons. The electrons are restricted to certain energy levels (orbitals) by rules of quantum mechanics. Electrons prefer to be in the lowest possible energy state (although they can't all occupy the ground state due to other rules). To take an electron to a higher state requires the addition of energy, which can be gotten by absorbing a photon of the right energy. Only the right energy will do, though, other photons will pass through the atom without interacting. Once the electron is excited, it will quickly lose its energy by emitting a similar photon. Each atom has a unique structure of energy levels, which means it interacts with a unique set of photons.

If a warm gas of atoms is placed in front of a hotter blackbody, it will scatter photons with its unique signature out of the blackbody (also called continuous or continuum, because it smoothly covers all wavelengths) spectrum, producing a set of absorption lines. If viewed by itself, the gas will only emit photons at its unique wavelengths, producing the same set of lines, but seen as emission lines (against the dark background). Thus we have Kirchoff's Laws:
1) an opaque body will produce a blackbody spectrum that gets brighter and bluer as the body gets hotter
2) if a cooler transparent gas is placed in front of the blackbody, it will produce a unique set of darker absorption lines in the blackbody spectrum
3) if viewed by itself, this gas will produce the same set of lines seen in emission

The fact that each atom produces discrete lines, and has a unique pattern, is the source of much astronomical information. Among the simplest is the use of the Doppler shift to give us the line of sight velocities of the emitting source. The speed of light (c) is always fixed at the same value: 3x10⁸ m/s. The Doppler shift works because the wavelength of the light will appear shorter if the source is moving toward us: each successive wave has less far to travel, so the waves arrive sooner than if the source were stationary and we interpret that as a shorter wavelength (or blueshift). Similarly, if the source is moving away the wavelengths appear longer (redshift). The fact that there are spectral lines with known rest wavelengths allows us to measure the shift of observed lines and deduce the component of velocity towards or away from us. The observed shift in wavelength (Dl = l_obs - l_rest) is related to the velocity by the formula: Dl = l_rest v/c .

As an example, the Earth moves in its orbit at 30 km/s. If we are observing a star directly in our path, the rest wavelengths of its spectral line at 600nm  will receive a Doppler shift of  Dl = 600(nm) x 30( km/s) / 3x10⁵ ( km/s) = 6x10^-2 ( nm). If the Earth is moving towards the star, this will be subtracted from the rest wavelength (a blueshift), so the observed wavelength of the line would be 599.94nm.