Quantum Chromodynamics (QCD) is the present theory of the strong interactions between quarks and gluons. To simulate QCD on a computer we need to discretise the field theory onto a space-time lattice. After outlining the standard Wilson action for lattice QCD, we describe the improved Clover fermion action with reduced discretisation errors. This thesis describes various techniques required to simulate lattice QCD and their implementation on the UKQCD Grand Challenge supercomputer Maxwell, which is a parallel computer consisting of 64 nodes. The ideas behind Monte Carlo (MC) simulation are introduced through their use to study spin systems in statistical physics. Various MC algorithms are outlined with particular emphasis on Stochastic Cluster MC and attempts to apply this to lattice gauge simulations. One of the best quantities to calculate in lattice QCD is the quark propagator. This requires the inversion of very large fermion matrices and takes an enormous amount of supercomputer time. We investigate a simple Red-Black preconditioning of the matrix and compare the performance of an Over-relaxed Minimal Residual inversion algorithm with various Conjugate Gradient algorithms. The quark propagators are calculated using Maxwell and we give details of our implementation of the inversion routines and the performance obtained. We present preliminary results from an investigation into the hadron mass spectrum. These are based on a sample of 9 gauge configurations on a 24³ x 48 lattice at β = 6.2. There are descriptions of how lattice masses are calculated and of Wuppertal smearing, which is a technique that may be used to improve the signal. We conclude with a comparison of the spectrum of masses obtained from the Wilson fermion action and the Clover action.