We discuss the design of the muon capture front end of the neutrino factory International Design Study. In the front end, a proton bunch on a target creates secondary pions that drift into a capture transport channel, decaying into muons. A sequence of rf cavities forms the resulting muon beams into strings of bunches of differing energies, aligns the bunches to (nearly) equal central energies, and initiates ionization cooling. The muons are then accelerated to high energy where their decays provide neutrino beams. For the International Design Study (IDS), a baseline design must be developed and optimized for an engineering and cost study. We present a baseline design that can be used to establish the scope of a future neutrino Factory facility.