Approximate formula to find velocity from cosmological redshift
This formula is exact if the expansion is linear ($a(t) = H_0 t$) and all peculiar velocities are zero. In that case, the comoving distance to the object is $$\int_{t_\text{then}}^{t_\text{now}} \frac{c\,\mathrm dt}{a(t)} = \frac{c}{H_0} \ln \frac{t_\text{now}}{t_\text{then}} = \frac{c}{H_0} \ln (1{+}z)$$ and the present recessional velocity is $H_0$ times that.
In the real world, the expansion has been not too far from linear, and recessional velocities are not too large, so it's reasonably accurate.