The XENON100 dark matter experiment uses liquid xenon (LXe) in a time projection chamber (TPC) to search for Xe nuclear recoils resulting from the scattering of dark matter Weakly Interacting Massive Particles (WIMPs). In this paper we present a detailed description of the detector design and present performance results, as established during the commissioning phase and during the first science runs. The active target of XENON100 contains 62 kg of LXe, surrounded by an LXe veto of 99 kg, both instrumented with photomultiplier tubes (PMTs) operating inside the liquid or in Xe gas. The LXe target and veto are contained in a low-radioactivity stainless steel vessel, embedded in a passive radiation shield. The experiment is installed underground at the Laboratori Nazionali del Gran Sasso (LNGS), Italy and has recently published results from a 100 live-days dark matter search. The ultimate design goal of XENON100 is to achieve a spin-independent WIMP-nucleon scattering cross section sensitivity of \sigma = 2x10^-45 cm^2 for a 100 GeV/c^2 WIMP.