We discuss molecular cloud formation by large-scale supersonic compressions in the diffuse warm neutral medium (WNM). Initially, a shocked layer forms, and within it, a thin cold layer. An analytical model and high-resolution 1D simulations predict the thermodynamic conditions in the cold layer. After $sim 1$ Myr of evolution, the layer has column density $sim 2.5 times 10^{19} psc$, thickness $sim 0.03$ pc, temperature $sim 25$ K and pressure $sim 6650$ K $pcc$. These conditions are strongly reminiscent of those recently reported by Heiles and coworkers for cold neutral medium sheets. In the 1D simulations, the inflows into the sheets produce line profiles with a central line of width $sim 0.5 kms$ and broad wings of width $sim 1 kms$. 3D numerical simulations show that the cold layer develops turbulent motions and increases its thickness, until it becomes a fully three-dimensional turbulent cloud. Fully developed turbulence arises on times ranging from $sim 7.5$ Myr for inflow Mach number $Mr = 2.4$ to $> 80$ Myr for $Mr = 1.03$. These numbers should be considered upper limits. The highest-density turbulent gas (HDG, $n > 100 pcc$) is always overpressured with respect to the mean WNM pressure by factors 1.5--4, even though we do not include self-gravity. The intermediate-density gas (IDG, $10 < n [{rm cm}^ {-3}] < 100$) has a significant pressure scatter that increases with $Mr$, so that at $Mr = 2.4$, a significant fraction of the IDG is at a higher pressure than the HDG. Our results suggest that the turbulence and at least part of the excess pressure in molecular clouds can be generated by the compressive process that forms the clouds themselves, and that thin CNM sheets may be formed transiently by this mechanism, when the compressions are only weakly supersonic.
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