  Einstein@Home aggregates the computer power of hundreds of thousands of
volunteers from 193 countries, to search for new neutron stars using data from
electromagnetic and gravitational-wave detectors. This paper presents a
detailed description of the search for new radio pulsars using Pulsar ALFA
survey data from the Arecibo Observatory. The enormous computing power allows
this search to cover a new region of parameter space; it can detect pulsars in
binary systems with orbital periods as short as 11 minutes. We also describe
the first Einstein@Home discovery, the 40.8 Hz isolated pulsar PSR J2007+2722,
and provide a full timing model. PSR J2007+2722's pulse profile is remarkably
wide with emission over almost the entire spin period. This neutron star is
most likely a disrupted recycled pulsar, about as old as its characteristic
spin-down age of 404 Myr. However there is a small chance that it was born
recently, with a low magnetic field. If so, upper limits on the X-ray flux
suggest but can not prove that PSR J2007+2722 is at least ~ 100 kyr old. In the
future, we expect that the massive computing power provided by volunteers
should enable many additional radio pulsar discoveries.
