Alternation of Generations
Sphenophytes are perennials, meaning they live for more than one year. Most of their reproduction is asexual. They clone themselves by extending horizontal roots called rhizomes, which grow into new individuals. Sexual reproduction in plants follows an "alternation of generations" or "alternation of phases" life cycle. The primary form of a sphenophyte is its sporophyte stage. In order for a sphenophyte to sexually reproduce, it must first go through an intermediate gametophyte stage by releasing spores.
Spores
Like an animal sperm or egg, the spores contain only half of the organism's genes. Unlike sperm and eggs, spores do not combine with other spores -- they grow into a multicellular plant with only one set of chromosomes. The resulting gametophyte is called a prothallus. Sphenophyte spores have appendages called elaters which help to embed them in the soil and clump together with other spores, which helps ensure that prothalli are close enough together to reproduce.
Prothalli
Prothalli are very small and short lived. Sexual reproduction takes place between prothalli when rainwater transports the sperm of one to the egg of another. The resulting zygote grows out of the prothallus into the sporophyte plant we recognize.