In the study of quantum mechanical systems, exact diagonalisation (ED) methods play an extremely important role. We have developed an ED code named DoQO (Diagonalisation of Quantum Observables). This code is capable of constructing and diagonalising the observables for spin 12 and spinless fermionic particles with many body interactions on arbitrary graphs using massively parallel distributed memory machines. At the same time, the code can exploit physical symmetries to reduce the size of the relevant basis set and provide useful physical information about each eigenstate. DoQO has been employed successfully to directly diagonalise systems with basis sets containing a billion elements. By exploiting symmetries it has been possible to perform calculations on systems with 36 spin 12 particles. Here we present essential background details, the structure and usage of DoQO, and a study of the performance characteristics of DoQO on different machines.