There is a little known fact that sponges are hermaphroditic. This means that they contain both female and male sex organs. The sponge will produce eggs and sperm at different times. The sponge will produce sperm (male) internally and then release them through the sponge's openings, when this is taking place the sponge appears to be smoking. Then, the sperm are captured by female sponges and the female transports the sperm by special cells to the eggs (female). This combination of sperm and egg then develops into a larvae, which is held inside the sponge until little baby sponges are produced. Wala! We have baby sponges. Sponges are not able to reproduce hermaphroditically until they are approximately three years of age.
Also, if needed, a sponge can reproduce asexually (internally) through internal buds called gemules. Each gemule can develop into a new sponge.