Beam chopping can be achieved by placing something like this in the beam-path:
The red dot is the cross section of the beam. As you can see, as the blade rotates, the beam is switched on and off.
The reason we chop is to distinguish background and beam. This is especially useful for atomic absorption spectroscopy, since the fire has to be in open air for safety reasons, and thus we cannot perform the experiment in complete isolated darkness. We must therefore measure the ambient background and subtract that away from our measurement.
In other types of experiments (e.g. IR, UV-Vis), we generally take one background on a blank sample, and use that for a whole series of measurements (i.e. we only do background once). In AAS however, since we are open to the surrounding environment, the background can change over time (e.g. the sun goes behind a cloud, and the room gets slightly darker). So we need to continuously measure the background, and this is why we need to chop the beam. Each measurement uses its own background.
Re: obtaining a spectrum. The most popular method is via "Fourier Transform" spectroscopy. Fourier Transform is a mathematical method that allows you to work magic with waves. We can fire one single pulse that contains all wavelengths, and via magic, work out the absorption at each individual wavelength. Of course, this is too advanced for VCE.
Older and/or simpler instruments use a 'scanning' method to obtain the spectrum. That means you can hit a button on the instrument to automatically make thousands of measurements at different wavelengths to give you a spectrum.
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