Structure
Above is a diagram of a bacterium cell, but it is not completely accurate for every cell because there is considerable variation in the components.
The chromosome (also called nucleoid) is found in the cytoplasm and never a nucleus and contains important genetic information.
Plasmids are rings of DNA additional to the chromosome, that are sometimes is a bacteria and sometimes not. They may make it resisant to antibiotics and they can move between different bacteria.
The flagella are also an optional part of the bacterium. They flick around like a tail and enable the cell to move.
Reproduction
Normally bacteria replicate by binary fission (a bit like mitosis). This process involves replication of the chromosome, cell growth and then division.
Some bacteria can produce spores (small cells that can develop into bacteria), but this is for extreme survivial purposes since these spores are resistant to high temperatures, drying up and chemical disinfectants.