The study of electron transport in low-dimensional systems is of importance, not only from a fundamental point of view, but also for future electronic and spintronic devices. In this context heterostructures containing a two-dimensional electron gas (2DEG) are a key technology. In particular GaAs/AlGaAs heterostructures, with a 2DEG at typically 100 nm below the surface, are widely studied. In order to explore electron transport in such systems, low-resistance ohmic contacts are required that connect the 2DEG to macroscopic measurement leads at the surface. Here we report on designing and measuring a dedicated device for unraveling the various resistance contributions in such contacts, which include pristine 2DEG series resistance, the 2DEG resistance under a contact, the contact resistance itself, and the influence of pressing a bonding wire onto a contact. We also report here a recipe for contacts with very low resistance values that remain below 10 Ω for annealing times between 20 and 350 s, hence providing the flexibility to use this method for materials with different 2DEG depths. The type of heating, temperature ramp rate and gas forming used for annealing is found to strongly influence the annealing process and hence the quality of the resulting contacts.