Most bacterial cells are prokaryotes. This means that their cells lack a nucleus or organelles. Instead, their genetic material is dispersed throughout the cytoplasm of the cell. Therefore, the division of the nucleus that occurs during division is not required for such bacterial cells.
Instead, these cells undergo a process known as binary fission (bi= two, fission = to split apart). The genetic material still replicates during binary fission. The cytoplasmic membrane then stretches, helping to divide the replicated genetic material. Once the DNA is separated, the cell begins to furrow in the center. Cross walls form at this furrow that then separate the prokaryotic cell completely.
This process can be visualized via this hyperlink.
There is also a resource down below which provides a more detailed explanation of binary fission.
Mitosis is the process by which the parent cell divides into 2 identical daughter cells. There are various phases of mitosis including prophase, prometaphase, metaphase, anaphase and telophase. Interphase is typically clubbed with mitosis and consists of processes (or phases) that prepare the cell for division. During prophase, chromatin begins to condense and centrioles start moving to the opposite ends of the cell. During prometaphase, the nuclear membrane dissolves and proteins attach to centromeres, which creates kinetochores. In the metaphase, mitotic spindle (formed during the prophase) aligns the chromosomes along the middle of nucleus. In anaphase, the chromosomes separate at kinetochores (formed in prometaphase) and move to opposite sides of the cell. New membranes are formed around the new cells during telophase. Finally, during cytokinesis, two identical daughter cells are formed.
Hope this helps.