In 2001, the D0 experiment entered a new era. Run II of the Tevatron at the Fermi National Accelerator Laboratory began, and the collider became the highest energy particle accelerator in the world. Accordingly, the D0 detector had already undergone a series of upgrades in order to fully exploit the physics now within reach. These included improvements to the tracking, calorimetry, muon detection and triggering capabilities. In the Standard Model, the Higgs boson is the last piece of the puzzle that remains to be discovered. The Higgs mechanism and consequently the Higgs boson is thought to be the fundamental ingredient by which particles acquire mass, and its existence (or lack of existence) is one of the most pressing issues in particle physics today. As such, one of the main goals of the Run II physics programme at D0 is to search for it. Armed with new accelerator capabilities, D0 will be able to impose tighter constraints on the mass of the Higgs, and perhaps even detect this elusive particle. If the Higgs does exist, it will be extremely difficult to find. One of the main challenges at a hadron-hadron collider is to reduce the large QCD background that masks the relatively tiny Higgs signal. Experimental evidence indicates that the Higgs mass is relatively low, in which case it will decay predominantly to a b$ar{b}$ quark-antiquark pair. The daughter products that must be used to reconstruct the parent Higgs are therefore likely to be heavy flavour b-quark jets whose energies must be known as accurately as possible. In the first part of this thesis consideration is given to these jets, in particular to the jet energy resolution and dijet mass resolution that they could offer. One way of investigating the necessary tools for such a Higgs search is to study a very similar decay to that of a low-mass Higgs particle: a Z boson decaying to a b quark and an anti-b-quark. This signal, not previously observed at the Tevatron, offers an ideal testbed in which to explore suitable triggering and analysis techniques. It also offers us the opportunity to further our understanding of b-quark jets in a hadronic environment, an element crucial to much of the physics at D0. To this end, the first search has been performed at D0 for the Z → b$ar{b}$ decay, using the initial 300 pb-1 of data from Run II. Triggers have been specifically designed and implemented for this purpose. Here we present evidence for Z → b$ar{b}$ decays. An excess of 1260 ± 130 (stat.) ± 260 (syst.) events is observed, which is in good agreement with Monte Carlo predictions and amounts to a Z → b$ar{b}$ signal of 4.3 standard deviations.