Despite what you may have seen in some textbooks, DNA is not built like a twisted ladder. The helix, or spiral, is an inherent feature of the DNA molecule. Notice, for instance, that in the picture below, that the groove on the left side of the picture is much larger than the right side. This is because the paired bases in the center meet each other at an angle.
DNA is a very large molecule; the image here shows only a tiny fraction of the typical molecule. If an entire molecule of DNA from the virus "bacteriophage lambda" were shown at this scale, the image would be 970 meters high. For the bacterium Escherichia coli, the image would be 80 kilometers long. And for a typical piece of DNA from a eukaryote cell, the image would stretch for 1600 kilometers, about as far as it is from Dallas to Washington, D. C.! Obviously such a large molecule is not fully stretched out inside the cell, but is wound around proteins called histones which protect the DNA.
You might also notice in the image that the two halves do not quite come in contact. In fact they are held together by hydrogen bonds, a sort of electrical attraction between partially negative atoms on the base of one side with the partially positive atoms on the other. Both sides have positive and negative charges. A single such pairing would not hold the molecule together well, but several million such bonds are quite effective. This also has the advantage that little effort is required to pull the two halves apart for replication, when the DNA is copied, and for transcription, when the DNA message is read. The message of DNA is the information from which the cell and its components are built.