1st Step: DNA Replication
After completion of the process of cell division, the two newly formed cells share the same amount of genetic material. This is achieved by the replication of the double stranded DNA of the parent cell. The two DNA strands are termed as the leading and lagging strands. In E.coli, DNA replicates in a bi-directional manner starting from the origin of replication. The two strands of DNA are unwound by a protein named DNA B protein. To prevent the two strands from pairing together, they are coated by single strand binding proteins.
The actual replication of the two strands begins with the help of a protein named DNA A. The point at which the replication begins is termed as ori C. The process of replication takes place in the direction of 5’ to 3’. The synthesis of leading strand which is oriented appropriately takes place without the need of a primer. However, the lagging strand synthesis takes place with the help of a primer, a single stranded RNA. Once the entire chromosome is replicated, the primers are removed and replaced by DNA. Now, the cell possesses two copies of DNA. The next step is the actual cell division i.e. the division of cytoplasm and the membrane.
You can get the details of the process at http://biology.kenyon.edu/courses/biol114/Chap01/cell.html.
2nd Step: Binary Fission
Cell division in bacterial cell ends with binary fission in which a constriction appears on the membrane at the point where the two chromosomes are joined. The constriction deepens further, dividing the cytoplasm and finally results in the formation of two cells with identical genetic composition. Each of these newly formed cells has genetic composition similar to that of the parent cell and is capable of producing new cells.
A thorough reading of this biology study guide will make you confident in solving bacterial cell division related problems. You can find some practice problems in the below given link.
http://www.tutorvista.com/search/questions-on-biology-cell-division&structure-of-chromosomes