Basalt columns form as sort of dessication cracks pretty much like drying mud cracks. The main difference is the temperature : basalt is cooling down quite rapidly and by doing so it starts shrinking. Of course this shrinking process starts at the surface, which is either air or more likely another, cool rock. And from that contact the shrinking process slowly develops into the depth, forming longer and longer columns. These can grow to many meter length, depending on the thickness of the original basalt lava flow. In some cases, such as the Devils Tower in Wyoming, the basalt columns may reach even 100 m length and more, but that surely is an exceptional length.
And there you have it folks at least when we climb Devil's Tower on Sept 6 we will know what we are hanging onto!