1. How do different animals breathe?
Lungs
eg. Man, whale, seal, bat, snake, dog, cow
Moist skin
eg. Frogs, toads, salamander, earthworm
Gills
eg. Fish, tadpole, mudskipper
Breathing tube
eg. Wriggler, water stick insect
Breathing holes
eg. Ant, dragonfly

2. Breathing Underwater
All animals breathe to obtain oxygen for their bodies and to expel carbon dioxide. Animals which live underwater have no problem in expelling carbon dioxide because it dissolves very easily in water. Their problem is how to obtain enough oxygen. The amount of oxygen dissolved in the water depends upon the water temperature but, in general, we can say that if the water is at 15°C there is 30 times more oxygen in the air than in water.

3. Gills
If the animal is not very active it could breathe through its skin as earthworms do on land. If, however, the animal is very active it may find that the skin does not let enough oxygen into the body. Animals which swim a lot need a considerable amount of oxygen to make the muscles work. More oxygen can enter the body if the skin has a greater surface. The skin can be given a bigger surface by making it stick out of the body as folds and projections. A gill is created when these folds and projections are given a blood supply. Because this type of gill sticks out into the water we call it an external gill. You can imagine that this type of gill could get in the way or be damaged if the animal moves around a lot.

4. Fishes have internal gills which are covered by an operculum
Fishes have internal gills which are covered by an operculum. To get enough oxygen the fish must make water flow across its gills. The fish does not breathe water in and out of its mouth.

5. The drawing shows the water entering the fish's mouth and crossing the gills. 

6. The above image is a close-up of one of the thin channels in the fish's gills.The channel that the water flows through is surrounded by blood vessels, that flow in the opposite direction. The oxygen leaves the water, and goes into the blood. From there, it is carried all around the body of the fish!

7. You can see that the fish's gills are feathery, which gives them a large surface. The gills also come in several layers. They can be very efficient at extracting oxygen from the water, allowing some fish to be very fast swimmers.

8. gill rakers
gill arch
gill filaments

9. Like humans, fish have water-proof skin
Like humans, fish have water-proof skin. This means they can't breathe through their skin like some other animals, like amphibians. Lungs don't work well in water, because it takes too much energy to move the water in and out of them. Instead, fish use their gills to get oxygen. Fish have a heart and circulatory system that is similar to that of humans, and it carries oxygen around to all the cells, just like in our bodies!

10. Neat Stuff
If there's oxygen in the water, then why can't humans breathe water? Because oxygen has to move from the water into our blood, which is much slower than when oxygen moves from the air into our blood. Gills are specialized to handle this slow movement, but our lungs can't pick up oxygen from the water fast enough to keep us alive, which is why we drown if we try to breathe water.
Resource :

11. Many aquatic invertebrates also have gills
Many aquatic invertebrates also have gills. Crustaceans, such as the crab, and molluscs, such as the mussel breathe using gills. 
A mussel also uses its gills for feeding. As the mussel sucks water into its shell to breathe, it also draws in the microscopic plankton which it filters and sends to its mouth. In this way a large mussel may pass 2,5 dm3 of water across its gills in an hour.

12. The Tracheal Gill
The young larvae of aquatic insects also have a kind of gill combined with their tracheal system. It is called a tracheal gill.
The insects do not have blood vessels passing through their gills, they have tracheae instead. These tracheae are filled with air just like the tracheae of air-breathing insects. They do not, however, open onto the outside world through spiracles. Instead they are completely closed off. Oxygen passes from the water, crossing the gills, and then moves into the air filled tracheae. From there the gas is transported around the body in the tracheal system.
Taken from :
Breathing through skin :