We compare the gas distribution, kinematics and the current star formation in a sample of 10 very faint (-13.37 < M-B < -9.55) dwarf galaxies. For five of these galaxies we present fresh, high-sensitivity, Giant Metrewave Radio Telescope H i 21-cm observations. We find that the large-scale H i distribution in the galaxies is typically irregular and clumpy, with the peak gas density rarely occurring at the geometric centre. We also find that the velocity fields for all the galaxies have an ordered component, although in general, the patterns seen do not fit that expected from a rotating disc. For all our galaxies we construct maps of the H i column density at a constant linear resolution of similar to 300 pc; this forms an excellent data set to check for the presence of a threshold column density for star formation. We find that while current star formation (as traced by H alpha emission) is confined to regions with relatively large [N-H i > (0.4-1.7) x 10(21) cm(-2)] H i column density, the morphology of the H alpha emission is in general not correlated with that of the high H i column density gas. Thus, while high column density gas may be necessary for star formation, in this sample at least, it is not sufficient to ensure that star formation does in fact occur. We examine the line profiles of the H i emission, but do not find a simple relation between regions with complex line profiles and those with ongoing star formation. Our sample includes examples of regions where there is ongoing star formation, but the profiles are well fitted by a single Gaussian, as well as regions where there is no star formation but the line profiles are complex. Finally, we examine the very fine scale (similar to 20-100 pc) distribution of the H i gas, and find that at these scales the emission exhibits a variety of shell-like, clumpy and filamentary features. The H alpha emission is sometimes associated with high-density H i clumps, sometimes the H alpha emission lies inside a high-density shell, and sometimes there is no correspondence between the H alpha emission and the H i clumps. In summary, the interplay between star formation and gas density in these galaxies does not seem to show the simple large-scale patterns observed in brighter galaxies.