SVM hyperplane margin
After we have 

$$w^Tx + b = \pm \delta$$

We can always divide everything by $\delta$,

$$\left( \frac{w}{\delta}\right)^Tx + \left( \frac{b}{\delta}\right)=\pm1$$

Now, we can set $\tilde{w}=\frac{w}{\delta}$ and $\tilde{b}=\frac{b}{\delta}$.

$$\tilde{w}^Tx+\tilde{b}=\pm1$$

This is as if we have set $\delta=1$ from the beginning.

The derivation of the distance formula has been given in equation $(19)$ in the article that you linked to and you might like to be more specific if you can't understand it. The distance should be $\frac{2\delta}{\|w\|}$ if $\delta$ is not set to be $1$.