We outline the LOFAR Long-Baseline Calibrator Survey (LBCS), whose aim is to identify sources suitable for calibrating the highest-resolution observations made with the International LOFAR Telescope, which include baselines >1000 km. Suitable sources must contain significant correlated flux density (≳ 50 - 100 mJy) at frequencies around 110-190 MHz on scales of a few hundred milliarcseconds. At least for the 200-300-km international baselines, we find around 1 suitable calibrator source per square degree over a large part of the northern sky, in agreement with previous work. This should allow a randomly selected target to be successfully phase calibrated on the international baselines in over 50% of cases. Products of the survey include calibrator source lists and fringe-rate and delay maps of wide areas - typically a few degrees - around each source. The density of sources with significant correlated flux declines noticeably with baseline length over the range 200-600 km, with good calibrators on the longest baselines appearing only at the rate of 0.5 per sq. deg. Coherence times decrease from 1-3 min on 200-km baselines to about 1 min on 600-km baselines, suggesting that ionospheric phase variations contain components with scales of a few hundred kilometres. The longest median coherence time, at just over 3 min, is seen on the DE609 baseline, which at 227 km is close to being the shortest. We see median coherence times of between 80 and 110 s on the four longest baselines (580-600 km), and about 2 min for the other baselines. The success of phase transfer from calibrator to target is shown to be influenced by distance, in a manner that suggests a coherence patch at 150-MHz of the order of 1 deg. Although source structures cannot be measured in these observations, we deduce that phase transfer is affected if the calibrator source structure is not known. We give suggestions for calibration strategies and choice of calibrator sources, and describe the access to the online catalogue and data products.