  In this paper, we investigate the conditions for the HI-to-H$_{2}$ transition
in the solar neighborhood by analyzing HI emission and absorption measurements
toward 58 Galactic lines of sight (LOSs) along with $^{12}$CO(1$-$0) (CO) and
dust data. Based on the accurate column densities of the cold and warm neutral
medium (CNM and WNM), we first perform a decomposition of gas into atomic and
molecular phases and show that the observed LOSs are mostly HI-dominated. In
addition, we find that the CO-dark H$_{2}$, not the optically thick HI, is a
major ingredient of the dark gas in the solar neighborhood. To examine the
conditions for the formation of CO-bright molecular gas, we analyze the
kinematic association between HI and CO and find that the CNM is kinematically
more closely associated with CO than the WNM. When CNM components within CO
line widths are isolated, we find the following characteristics: spin
temperature $<$ 200 K, peak optical depth $>$ 0.1, CNM fraction of $\sim$0.6,
and $V$-band dust extinction $>$ 0.5 mag. These results suggest that CO-bright
molecular gas preferentially forms in environments with high column densities
where the CNM becomes colder and more abundant. Finally, we confront the
observed CNM properties with the steady-state H$_{2}$ formation model of
Sternberg et al. and infer that the CNM must be clumpy with a small volume
filling factor. Another possibility would be that missing processes in the
model, such as cosmic-rays and gas dynamics, play an important role in the
HI-to-H$_{2}$ transition.
