It may take place by budding or fission.
Budding is the most common method of multiplication and takes place when food supply is plenty and environmental conditions are suitable. At first a small outgrowth or protuberance is formed at one end of mother cell.
The nucleus divides in the middle by constriction and the nuclear membrane does not breakdown. A portion of the constricted nucleus along with other cell organelles enters the bud. Next, the cytoplasmic connection between the parent cell and the bud is closed by formation of wall material.
The bud then may assume normal size which may also undergo budding in the same manner. As a result, chain of yeast cells or buds is formed within a short time and they remain attached with each other for sometime forming pseudo-mycelium. The buds may separate from the parent cells to form one celled yeast.
Fission involves division of yeast cell into two by transverse division. The mother cell first elongates. After reaching a definite size, its nucleus divides into two by mitotic division. The two daughter nuclei move apart. A transverse partition wall is formed in the middle and the mother cell divides into two parts. Each part with a nucleus separate from the other and form two independent yeast cells. The process is like the bacteria that divide by fission.