I assume with EM you refer to electromagnetic?
You are right that the EEG (electroencephalogram) is a tiny signal. When about 50.000 neurons fire simultaneously, it possible to see a change in the measured signal. Typical EEG amplitudes are in the microvolt range.
Now, when the EEG is recorded, it is a function of time. You could for example collect data from 64 sensors, using a typical sampling frequency of 1000 Hz, and obtain 100000 samples from each sensor during a 100 second measurement.
So, what are alpha, beta, gamma, etc? When the recorded EEG signals are transformed into the frequency-domain (using the discrete Fourier transform), the signals become represented as a function of frequency. The obtained frequency range is half of the sampling frequency (according to the sampling theorem). So, with $f_s = 1 $ kHz you may observe frequencies from $0$ to $500$ Hz. Now, to make it easier to discuss about specific parts of the frequency range, they have been given names: delta refers to frequencies from 0-4 Hz, alpha to frequencies 7-15 Hz etc. So, these are just arbitrary names for different frequency ranges. (And yes, some processes do occur in quite exact ranges.)
So what effects what the EEG spectra will look like? Just about everything. From a short segment of data, it is rather impossible to say anything. This is why many paradigms do averaging: for example, you are presented a sound 100 times, and the repetitions are averaged to cancel uncorrelated noise. Have a look at the so called oddball paradigm, for example. Single-trial and continuous recording are also done today, but they are more difficult to analyse.
(Side note: since you asked about electromagnetic brain waves, have a look at magnetoencephalography too..)
For reference, see e.g. Luck (2005), An Introduction to the Event-related Potential Technique. Fourier transforms, sampling theorem, and signal averaging are well covered in Wikipedia.