Orthonormal basis of linear subspace

Question

For a rectangular matrix $M_{i\mu}$ where $i=1,...,m$ and $\mu=1,...,n$ and $n>m$, consider the following $n-m$ dimensional linear subspace of $\mathbf{R}^n$: $$V=\{\vec x\in \mathbf{R}^n:M\vec x=0\}.$$ Clearly $V$ is spanned by $n-m$ orthonormal vectors $\{\vec e_1,...,\vec e_{n-m}\}$. How can one find an explicit set of such vectors given $M_{i\mu}$?