Mermaids are humans from the waist up, but fishes from the waist down. The boundary between the human area and fish area happens in the pelvis; this area is part human-part fish (the outside of this area is fish). Areas above the pelvis are human, and areas below the pelvis are fish.
How mermaids breathe ====================
Mermaids have gills similar to that of fishes. This enables them to breathe underwater. However, they can also breathe surface air for extended periods of time (some fishes can do this too). They do have to keep their gills moist however; the moisture supports the gills, which collapse without it. Mermaids to have an ability to retrieve moisture from the air somewhat for this purpose; consequently they only need to drink water slightly more often than humans do. Mermaids' skin is also able to tolerate being constantly wet (stay in the sea a few days and see what happens to your skin). These are the only aspects of mermaids' upper bodies which are different from humans.
Mermaid tails =============
Mermaid tails are fish tails. Even though mermaids are warm-blooded, their tails are still cold-blooded. Their tails need moisture regularly to maintain integrity (just like fish tails do), especially the scales. However, a mermaid can stay out of water (in a humid area) for up to twelve hours (depends on the mermaid) without loosing tail integrity (in the episode "Metal Fish" at the end of the episode Ariel sat on a rock looking out into the distant horizon from afternoon until evening).
How mermaids reproduce ======================
Females have human internal reproduction organs; however the vagina is slightly shorter, and the common urogenital opening (the urethra merges with the vaginal canal near the opening) is at the front. The opening can stretch as much as a human vaginal opening; mermaid babies are born live (as opposed to hatched from eggs). A clitoris (which is the same color as the tail) is slightly below the urogenital opening, and an anus is above the urogenital opening. Mermaid vaginas are slightly smaller than human ones (since male mermaid penises are smaller, explained below), so they tend to be more sexually satisfying to human males.
Males do have a penis, but it is almost as small as a human female clitoris and is the same color as the tail; it is hardly visible (this is the only plausible explanation to why no one has ever seen a penis on any of the male mermaids). It is used for urination, as well as sexual intercourse. The testicles are inside the tail, as opposed to the pelvis, since they require a slightly lower temperature to function properly (the human and pelvis part is warm-blooded, but the tail is cold-blooded). The anus is above the penis.