The basic idea of the GA is simple enough. Start with a representation of a solution as a sequence of bits that can be combined in the same way as DNA, i.e. using exchange and mutation. Next set up a population of solutions and test them against the problem. Finally weed out the poor performers and allow the best of the rest to mix their genetic material to product the next generation of solutions.
If you go through enough generations the solutions should keep getting better as the population evolves towards a better fitness.