I don't understand how the first two quantum numbers fit into describing atoms.

There are 4 quantum numbers. Each one describes a specific electron's position relative to its nucleus.
The first one, "principal quantum number" describes the distance the talked about electron is from the nucleus. When it's described with maths it is given the letter "n". "n" if you read it would translate to "principal quantum number" you can write either down its really just a preference. To interpret this description, for example if you were told n=1, you should think of the nucleus with rings around it - like the solar system, the sun being the nucleus and the planets being different electrons - and the electron described with n=1 should be found in a space that has the distance of the first ring from the nucleus.
The second one, "Angular momentum quantum number" describes the shape of space that the talked about electron might be present in (shape of orbital). So if the principal quantum number, n, is big then this just means the size of shape that the electron may be present in will be far from the nucleus. The shape of the orbital will not change unless the angular momentum number changes. When it is described with maths it is given the letter "l". But the letter l can equal a number (l=0, l=1, l=2....) and these numbers describe a picture of an orbital shape that is described by a letter (s, p, d, f), respectively. So really by maths: L=0 relates to orbital shape "s" (which can be drawn on the whiteboard)and so on..