I am recently reading the code of TFOCS (Templates for First Order Conic Solvers). You can find it here on Github. One of the key parts in TFOCS is to find the projection of a given point $x_0$ (in $R^n$ or $R^{m \times n}$) onto a convex set $\mathcal{C}$. I will try to make a neat summarization and give concrete (and useful) examples of projections on different convex sets.