This is an excerpt from an article I found on Salty Underground.com

Asexual

Aiptasia reproduce asexually by pedal laceration. Small masses of cells are pinched or torn off the margins of the pedal disk forming small buds. These grow slowly into buds and within a week or two after completely separating from the foot the bud develops a mouth and small tentacles and begins to feed on its own. Some of these clones will release and be distributed in the water column to colonize other locations. Additionally, Aiptasia demonstrates a preferential tolerance to its own clones and will not sting them. This allows large groupings of Aiptasia clones to form as a result of asexual reproduction.

Unlike some cnidarians, Aiptasia are extremely successful in generating or regenerating an entire animal from a single cell. It is because of this that physical removal is so difficult to perform successfully.

Aiptasia increase asexual reproductive basal lacerates during times of extreme stress such as low oxygen, decreased circulation during power failures, low lighting situations, attack by predators or when the aquarist attempts physical or chemical methods of removal.

Sexual

While there is little scientific documentation on the sexual reproduction within Aiptasia, general observations indicate the sexual reproduction may occur in two forms.

In the case of the well-studied Aiptasia pallida and Aiptasia pulchella, individuals are dioecious, meaning that individuals are of separate sexes. During spawning, anemones release their gametes into the water where fertilization occurs. The resulting zygote becomes a free swimming planula larva which eventually settles onto a suitable substrate and undergoes metamorphosis to become a small polyp. Newly produced larvae are aposymbiotic meaning they do not contain symbionts. The larvae or newly settled polyps acquire symbiotic algae from the environment.

In certain species of Aiptasia fertilization may be internal, in the coelenteron. Male gametes are released from male Aiptasia into the water column. These gametes are non-buoyant and settle to fertilize the female gametes within other Aiptasia. These gametes develop internal to the Aiptasia into Planula Larva, receiving nourishment from the hosting anemone. When conditions are optimal (light and nutrients are high), or during physical attack (as when an aquarist is attempting to remove them), these larva are released into the water column to start growing and colonizing other parts of the reef.