Binary fission is the main process by which bacteria asexually reproduce. It can be summarized as a process in which the cell enlarges, its DNA is replicated and the cell splits into two cells, each with one copy of the DNA. Bacteria generally only undergo binary fission under favorable circumstances.
Binary fission involves the use of cellular machinery to move the replicated DNA to opposite sides of the cell, and then to split the cell in two. Multiple units of a special type of ring are assembled at the center of the dividing cell, and these then begin to contract, pinching the cell membrane closed between each daughter cell. Other cellular machinery ensures that the DNA is not damaged as the cellular membrane is constricted. In many types of bacteria a new cell wall is also built between the daughter cells as the cell membrane is pinched closed.
While binary fission is the most common form of reproduction for bacteria, it's not the only method used. Some species of photosynthetic bacteria instead grow to a very large size and then divide multiple times within a round shell before dispersing. Other species branch out and reproduce by budding, forming much smaller daughter cells rather than two equal daughter cells from a dividing cell.