A chromosome is a very long DNA molecule which contains hundreds or thousands of genes as well as some specialized protein molecules which hold it in shape, etc. In organisms more complex than bacteria, the chromosomes are usually paired, so that each gene is represented twice -- except that the two paired chromosomes could have slightly different genes.
It has long been possible to determine the order of genes on the string using an extraordinarily laborious method, at least for genes whose function is known. The idea is that characteristics that tend to be inherited together are coded by genes that must be close together on the same chromosome, and characters that are inherited more or less independently are controlled by genes that are far apart, or are on different chromosomes. Scientists made rough genetic ``maps'' of simple organisms by studying millions of matings.
The favorite test animal for these experiments was the fruit fly, Drosophila melanogaster. It breeds very quickly, requires little food and little space. You don't need much complicated or expensive equipment to do experiments with fruit flies. They also have a most remarkable and useful peculiarity. In the salivary glands of the fruit fly, each chromosome is not a single DNA molecule, but hundreds or thousands of identical DNA molecules packed together. These giant chromosomes can be seen under a microscope. They show light and dark bands that help to locate the individual genes very precisely.
Today we can make exact maps with much less work using modern biotechnology methods. The complete map of human genes was recently finished. There are also complete genetic maps known for about a dozen other species, including E. coli bacteria, tiny flatworms, rice, and fruit flies.
The DNA of bacteria are not packaged in chromosomes. Instead the long string of DNA letters closes on itself to form a circle, with no beginning or end.