How do organelles divide?
Well, the nucleus does not divide per se. Remember, the nuclear membrane dissolves during mitosis. It starts reforming after metaphase. Here is a review detailing the process and the mechanisms which are known. By extension, the Endoplasmic reticulum gets portioned as it is derived from the nuclear membrane.
Organelles also rely on the cytoskeleton and associated motor proteins for distribution between the daughters. A debated aspect in this regard is whether the organelles are distributed at random or is there an active process that ensures similar distribution between the daughters.
Finally, on to mitochondria. Till this point we have assumed symmetric cell division i.e. both daughters get almost equal amounts of maternal material. But in stem cell divisions, the non-stem daughter is smaller in size. Interestingly, this paper shows that the stem like daughter gets younger mitochondria (less damaged mitochondrial DNA).
As you can see, it is impossible to cover all the organelles in a single answer. And we are not even considering physiological differences between different cell types. Cheers!