See a previous Q&A: Why do brains oscillate within specific frequency ranges?
I think that answer covers much of your question; I'll try to cover the rest here. In short, the names gamma/beta/alpha/theta/delta are just that: names of parts of a spectrum, just like colors red/green/blue. "Alpha waves" aren't necessarily a real, discrete thing, it's just a name given to oscillations in a particular frequency band which may or may not be due to a "real" oscillation: even a random system produces waves of many frequencies.
The power spectrum of noise in the brain is typically "pink" which means it falls off with ~1/f or 1/f2.
To see "real" elevations in a power spectrum, you need to plot the whole spectrum and look for "bumps." I just grabbed one from a random paper, and although I don't like how these data are plotted without a log scale, it does show peaks in the spectrum nicely:
Image adapted from Cajochen et al 1995; annotations mine.
As far as the amplitude of these "waves" - that entirely depends on your recording system, skull geometry, and other technical issues specific to a particular recording: the actual amplitude in volts is not really important. Therefore, typically one normalizes the power spectrum and either compare across conditions in a recording (that is, keeping the recording system constant and looking at different epochs), or normalizes the entire spectrum to "total power" to compare between recordings.
It almost never make sense to compare power in different frequency bands, though, in saying whether a frequency is "dominant": there is no meaning to delta being higher than beta, for example, besides the power law relationship where power is almost always higher at lower frequencies (except for extreme cases like the alpha peaks in the image above). What is relevant, however, could be when "in condition A, delta is higher than delta in condition B, and beta in condition A is lower than beta in condition B": relative comparisons are key. The exception is when you have prominent peaks, like in the image above.
Cajochen, C., Brunner, D. P., Krauchi, K., Graw, P., & Wirz-Justice, A. (1995). Power density in theta/alpha frequencies of the waking EEG progressively increases during sustained wakefulness. Sleep, 18(10), 890-894.