Almost all prokaryotes undergo a type of asexual reproduction called binary fission. Binary fission is very similar to the process of mitosis in eukaryotes. However, since there is no nucleus and the DNA in a prokaryote is usually just in a single ring, it is not as complex as mitosis. Binary fission starts with a single cell that copies its DNA and then splits into two identical cells.
This is a very fast and efficient way for bacteria and similar types of cells to create offspring. However, if a DNA mutation were to occur in the process, this could change the genetics of the offspring and they would no longer be identical clones. This is one way that variation can occur even though it is undergoing asexual reproduction. In fact, bacterial resistance to antibiotics is evidence for evolution through asexual reproduction.