The quantitative assessment of the entanglement in multipartite quantum states is, apart from its fundamental importance, a practical problem. Recently there has been significant progress in developing new methods to determine certain entanglement measures. In particular, there is a method-in principle, analytical-to compute a certified lower bound for the three-tangle. The purpose of this work is to provide a manual for the implementation of this approach and to explicitly discuss several analytically solvable cases in order to gauge the numerical tools. Moreover, we derive a simple analytical bound for the mixed-state three-tangle.