How to find poles of transfer function by looking at the step response?
There are two things to determine: the frequency $f_n$ (or angular frequency $\omega_n$) and the $Q$.  Approximately (for a high $Q$ system like the one pictured):

1) period $T$ is the time between successive peaks. $f_n=1/T$, and $\omega_n=2 \pi f_n$. 

2) ratio of successive positive (or negative) peaks (measured relative to steady-state) $ 1- \delta = e^{-2 \pi /(2Q)} $, or, for high $Q$, $ Q \approx \frac{\pi}{\delta}$.  [Example: If $\delta=0.1$ (10% amplitude decay per cycle), $Q \approx 30$.]

The poles are at $ \omega_n \left[-\frac{1}{2Q} \pm i \sqrt{1-\frac{1}{(2Q)^2}} \right] $, or in radial coordinates: $(\omega_n, \pi \pm \tan^{-1}{\sqrt{4Q^2-1}})$.

[There's also a pole at zero for the step response. Per bobuhito's comment, this pole is not part of the transfer function.]