The highly stable spin of neutron stars can be exploited for a variety of (astro)physical investigations. In particular, arrays of pulsars with rotational periods of the order of milliseconds can be used to detect correlated signals such as those caused by gravitational waves. Three such 'pulsar timing arrays' (PTAs) have been set up around the world over the past decades and collectively form the 'International' PTA (IPTA). In this paper, we describe the first joint analysis of the data from the three regional PTAs, i.e. of the first IPTA data set. We describe the available PTA data, the approach presently followed for its combination and suggest improvements for future PTA research. Particular attention is paid to subtle details (such as underestimation of measurement uncertainty and long-period noise) that have often been ignored but which become important in this unprecedentedly large and inhomogeneous data set. We identify and describe in detail several factors that complicate IPTA research and provide recommendations for future pulsar timing efforts. The first IPTA data release presented here (and available online) is used to demonstrate the IPTA's potential of improving upon gravitational-wave limits placed by individual PTAs by a factor of ~2 and provides a 2σ limit on the dimensionless amplitude of a stochastic gravitational-wave background of 1.7 × 10-15 at a frequency of 1 yr-1. This is 1.7 times less constraining than the limit placed by Shannon et al., due mostly to the more recent, high-quality data they used.