An excellent question. Mitochondria divide by simple fission, splitting in two just as bacterial cells do, and although the DNA replication strategies are a little different, forming displacement or D-loop structures, they partition their circular DNA in much the same way as do bacteria. Mitochondrial reproduction is not autonomous (self-governed), however, as is bacterial reproduction. Most of the components required for mitochondrial division are encoded as genes within the eukaryotic (host) nucleus and translated into proteins by the cytoplasmic ribosomes of the host cell. Mitochondrial replication is thus impossible without nuclear participation, and mitochondria cannot be grown in a cell-free culture. A tight control over mitochondrial division is essential to prevent uncontrolled mitochondrial replication, which could easily lead to destruction of the host cell. This provides an elegant illustration of the co-evolution between the mitochondria and their hosts in the evolution of the eukaryota.

Mitochondria and chloroplasts divide by fission, much like bacteria. When the cell divides, the mito and chloro are distributed to the daughter cells.
Most of the proteins in the mito and chloro are encoded by the nuclear genome and they are imported. They are translated on ribosomes in the cytoplasm. The newly formed protein has a sequence of amino acids at the N-terminus that acts as an import signal - it is recognized and bound by the import machinery on the membrane of the mito or chloro and the protein is pulled inside.

Wow, what a good question! I never thought to ask about that when I took my biology classes in college. Doing some research, I found that this is an area scientists don't know much about. I'm not at all knowledgeable on the subject, so I got a friend of mine to help me out (Ed Lowry, a graduate student in the Department of Ecology, Evolution and Marine Biology at UC Santa Barbara). Remember that chloroplasts and mitochondria are known as organelles (another word for membrane-bound bodies within a cell), and the cytosol is the liquid within the cytoplasm, or the interior of the cell. Here's what Ed had to say:

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Some old texts of mine bring a few interesting bits to light. 3&4 are the most pertinent ones. All quotes are from Ch. 7 of Molecular Biology of the Cell, by Alberts and his buddies:

1) Mitochondria in the cell are not strictly individuals. They are "remarkably plastic organelles, constantly changing their shape, even fusing with one another and then separating again."

2) Mitochondria and chloroplasts are dependent for the most part on proteins synthesized from nuclear DNA and imported into the organelle. Some proteins are encoded by organelle DNA and synthesized in the organelle. Interestingly, "no protein is known to be exported from mitochondria or chloroplasts to the cytosol."

3) A class of yeast mutants called "cytoplasmic petite mutants" entirely lack DNA in their mitochondria. "Although petite mutants cannot synthesize proteins in their mitochondria, and therefore cannot make mitochondria that produce ATP, they nevertheless contain mitochondria that have a normal outer and an inner membrane with poorly developed cristae [the folds in the membrane]... Such mutants dramatically demonstrate the overwhelming importance of the nucleus in biogenesis. They also show that an organelle that [here's the important part!] divides by fission can replicate indefinitely in the cytoplasm of proliferating eukaryotic cells even in the complete absence of its own genome."

4) "Overall control [of organelle replication] clearly resides in the nucleus... the nucleus must regulate the number of mitochondria and chloroplasts in the cell according to need... Although these regulatory aspects are crucial to our understanding of eukaryotic cells, we know relatively little about them." Well, shoot.

For most cell types there is what is called a "restriction point" in the cell cycle. Prior to this point the cells might maintain a sort of status quo if, for example, the environment is unfavorable for growth. Past this point, an internal change takes place which commits the cell to replicate its DNA and divide.

A signaler called "S-phase activator" (I guess people with lots of imagination become screenwriters or clothing designers) appears in the cytoplasm prior to DNA replication. (the book says it may be a group of molecules and not a single one, but it doesn't specify their identities). The major control molecules have been related to a class of genes termed "cdc" genes, for "cell-division cycle", of which there are more than twenty.

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We know from some studies on plants that nuclear, mitochondrial and chloroplast DNA replication takes place in parallel, and must therefore be coordinated. They don't necessarily take place at the same rate (there are more mitochondria and chloroplasts than nuclei per cell), but the relative ratio of these three organelles remains constant (although the ratio varies with cell type: e.g. leaf versus root cells). What coordinates DNA replication at different sites within a cell to maintain this ratio is not known. The two options that come to mind are (1) that nuclear, chloroplast and mitochondrial DNA replication are triggered by the same chemical signal or (2) that nuclear DNA replication triggers chloroplast and mitochondrial DNA replication.