How do you find maximal orders in quaternion algebras?

For semisimple algebras over $\mathbb{Q}$, there is a general algorithm due to Gabor Ivanyos and Lajos Ronyai, described in Finding maximal orders in semisimple algebras over $\mathbb{Q}$ and implemented in the computer algebra system Pari/gp. For quaternion algebras, there is a dedicated algorithm due to John Voight, described in Identifying the matrix ring: algorithms for quaternion algebras and quadratic forms and implemented in the computer algebra system Magma.

See Example B on page 9 of these notes: http://www.math.polytechnique.fr/~chenevier/coursIHP/chenevier_lecture6.pdf

Let $D =\left(\frac{−1,−11}{\mathbb{Q}}\right)$ be the quaternion algebra with discrimimant 11. A discriminant computation shows that a maximal order $O$ is given by $\mathbb{Z}[z] + i\mathbb{Z}[z]$ where $z = \frac{1+j}{2}$.

Sorry I couldn't give a more general answer.