X waves, spatiotemporal generalization of the monochromatic Bessel- (or Durnin-) type beams, are known in linear acoustic, microwave and optics for their unique property of defeating both spatial and temporal spreadings. Recently, we brought to the attention that X-type waves are also the key to understand the spatiotemporal dynamics observed in the nonlinear (high intensity) regime. Indeed, X waves represent the normal-propagation mode for a wide class of parametric interactions described by hyperbolic nonlinear models featuring spatial self-focusing and temporal self-broadening. Here, we provide a complete and detailed description of the experiment in which the spontaneous appearance of X waves has been observed. The experiment concerns frequency doubling of a 170-fs, 50-mum standard laser wave packet in a 22-mm lithium triborate crystal, tuned for second-harmonic generation with positive phase mismatch, positive group-velocity dispersion, and large group-velocity mismatch. Conventional beam-profile and autocorrelation measurements at the crystal output face show evidence of spatiotemporal self-trapping. The characterization of the free-space propagation reveals sub-Gaussian diffraction and pulse broadening, consistent with the presence of angular dispersion. Space-resolved autocorrelations indicate the generation of an X-type profile.