Fungi can reproduce either sexually or asexually. Fungi sexually reproduce when male and female cells come together. Fungi asexually reproduce via spontaneous growth, like new fungus growing from the parent fungus.
Fungi reproduce via spores. Male and female cells come together to turn into spores. These spores leave the fungi and land on a good growing environment. Sometimes this could be bread, fruits, or the ground. When conditions are right, spores grow into fungi.
When someone looks under a mushroom, she sees what look like gills. These gills hold spores. Had these mushrooms remained in the environment, these gills would've served as spore nurseries. Spores would fall from these gills and land where the next set of mushrooms would grow.
Puffballs provide another tactic for fungi to reproduce. The "powders" inside this puffball are actually spores. When these spores are ready, the "balls" open up. Rain comes down and completes the job. Raindrops hit these spores; the spores ride the wind; then these spores float to the ground.
The fungi have what's called a mycelium, which has parts that produce male cells. The mycelium also has parts that produce female cells. These parts join together to start reproduction. This could take anywhere from weeks to years, depending on the type of fungi. The male cell and the female cell come together to form a diploid cell. Diploid means that the cell has one nucleus and two different groups of chromosomes. Normally, a cell has one nucleus and one set of chromosomes.
This cell divides into two, then develops into spores. These spores land on a suitable growing spot, and the fungi life cycle starts over again.