Sexes are generally separate in sea anemones. The typical reproductive pattern is one where both sexes spawn into the sea where fertilization occurs. Within a few days of fertilization, a swimming motile larva called a planula is formed. Depending on the species, the larva may or may not feed. Eventually the larvae will metamorphose into a small sea anemone and take up existence in the benthic environment. Asexual reproduction is common in some anemones, including the bulb tipped anemone, Enatacmaea quadricolor, which may reproduce by splitting into two or more clonal descendants. Such cloning is absent or very rare in other host sea anemones. Unfortunately there really isn't any good data on each species with regards to reproduction. We know that the E. Quad can be a prolific splitter, and many of the mushroom's and ricordia's do this as well. Some may even move and leave a piece of themselves behind which become an anemone. From my limited understanding of most of the hosting style anemones it usually takes something stressful or traumatic for this to happen. But that's not to say that it is impossible.
According to one article that I read "Proceedings of IUCN/WCPA-EA-4 Taipei Conference March 18-23, 2002, Taipei, Taiwan" Conylactis anemones were capable of sexual and asexual reproduction.
Thomas