A parent yeast cell forms a growth, or bud, on its surface. One of these nuclei transfers into the growing bud, which eventually pinches off. One yeast cell can produce up to 24 daughter cells. Other fungi reproduce through spore formation. Spores are kind of like seeds in that they can be carried on the wind or rain, spreading the fungus to new places.
Some species can do both sexual and asexual reproduction, depending on environmental conditions.
Microbes in the protist category reproduce in a number of ways. Algae, for example, can reproduce without sex. The nucleus of the algal cell divides by mitosis and moves to opposite ends of the cell. Some species can reproduce sexually. Some do both.