Explain how the process of asexual reproduction works. what events must a cell go through to successfully reproduce asexually?

Asexual reproduction happens in prokaryotic microorganisms (bacteria) and some eukaryotic single-celled and multi-celled organisms. There are several ways by which animals reproduce asexually. The processes are briefly given in the explanation section.

Explanation:

Fission: It is also called binary fission. It occurs in prokaryotic microorganisms and in some invertebrate, multi-celled organisms. In this process, after a certain period of growth, an organism divides into two separate organisms. Some unicellular eukaryotic organisms do binary fission by the mitosis process.

Budding: Budding is a form of asexual reproduction where an outgrowth of a part of a cell or body region is formed.  It leads to a separation from the original organism, which produces two individuals. Budding occurs commonly in some invertebrate animals such as hydras and corals.

Fragmentation: Fragmentation is simply the breaking of the body of an organism into two parts. If the animal is able to do fragmentation, and the region is big enough to make fragmentation, a separate individual will be produced.

Parthenogenesis: Parthenogenesis is a type of asexual reproduction where an egg develops directly into a complete individual without passing the fertilization process.