How do I find the second order transfer function from this step response diagram?
From the step response plot, the peak overshoot, defined as

$$M_p = \frac{y_{peak}-y_{steady-state}}{y_{steady-state}}\approx\frac{1.25-0.92}{0.92}=0.3587$$
Also, the relationship between \$M_p\$ and damping ratio \$\zeta\$ (\$0\leq\zeta&lt;1\$) is given by:

$$M_p=e^\frac{-\pi\zeta}{\sqrt{1-\zeta^2}}$$

Or, in terms of \$\zeta\$:

$$\zeta=\sqrt{\frac{\ln^2M_p}{\ln^2M_p+\pi^2}}$$
So, replacing that estimated \$M_p\$:
$$\zeta\approx0.31$$
Also, from the step response plot, the damped natural frequency is aprox. 0.5 Hz or \$\pi\$ rad/s. The relationship with the undamped natural frequency is:
$$\omega_n=\frac{\omega_d}{\sqrt{1-\zeta^2}}\approx3.3 rad/s$$
Finally, the gain \$G_{DC}=y_{steady-state}\approx0.92\$

A standard second order transfer function has the form:
$$H(s)=G_{DC}\frac{\omega_n^2}{s^2+2\zeta\omega_ns+\omega_n^2}$$
Putting the obtained values:
$$H(s)\approx\frac{10}{s^2+2s+11}$$
Compare the step response below with that supplied by you: