General methods of Analysis for FTIR Results
Let me start by saying that the XeF$_4$ is a standard example of group theory applied to IR, which is generally treated in Uni courses, for which you can find plenty of notes on the web. For these reasons, I will not explain it, but you can rather put a bit of effort and read it yourself.

In general, the level of information you can extract depends on the nature of the molecules you analyse. For example, for organic molecules, the analysis is qualitative and limited to functional group identification. This is because usually they have a high number of atoms, thus there will be many vibrations. Since the chemical composition is quite homogeneous, all these vibrations have similar frequencies, and they overlap. Thus a quantitative analysis is difficult, and the only information you extract concerns some particular bond whose signal is isolated from the mess (usually carbonylic and carboxylic bonds, triple bonds, X-H bonds). An additional problem lies in conformational flexibility.

Now, for molecules like yours, which are small, have few vibrations, are symmetric etc, you can achieve a very detailed level of analysis. But, as I said, I will not discuss it, since you can read it yourself with a quick google search.
The basic thing to keep in mind is the frequency of oscillation of a classical harmonic oscillator, given by

$$ \omega = \sqrt{\frac{k}{\mu}} \\
\mu = \frac{m_1 m_2}{m_1 + m_2}$$

where $k$ is the force constant of the bond, and $\mu$ is its reduced mass.
So, what this tells you is that stronger bonds vibrate at a higher frequency. It also tells you that bonds involving lighter atoms vibrate at a higher frequency. Another thing that you can deduce is that bending frequencies are lower than stretching frequencies.
So, to give you a hint, what you can say immediately by looking at those frequencies you reported is that the 586 cm$^{-1}$ vibration is a stretching.