The droplet epitaxy (DE) method was applied to misoriented GaAs(111)B substrates to fabricate self-assembled GaAs quantum dots (QDs) by molecular beam epitaxy. In the first step the planar deposition of GaAs and AlGaAs on the substrate was optimized to yield smooth surfaces. The next step was to fabricate GaAs QDs on an AlGaAs surface by DE. As DE is a multistage process, each step was optimized and analyzed individually using atomic force microscopy. A variation of Ga droplet deposition temperatures was investigated while the amount and rate of deposited material were kept constant. A clear relation to the droplet density was found and interpreted using a scaling law approach. Droplet shape and symmetry were investigated and a set of parameters, which keeps a droplet density suitable for structural and optical characterization, was identified. The crystallization process from droplets to QDs was varied in temperature and time. For complete crystallization extremely low temperatures and long times turned out to be necessary. When compared to reports of similar experiments on (100) and (111)A substrates, strongly decreased temperatures had to be used on (111)B to achieve similar results in both steps. After capping and ex-situ annealing the QDs were optically active and showed photoluminescence. Ensemble measurements of the QDs with broad emission spectra around 780 nm could be acquired at 14 K. Single-dot luminescence revealed excitonic linewidths of 0.2 meV.