How do animals mate?

This depends on the animal. By 'animal' I am excluding simple organisms that reproduce by dividing.

Slugs, snails and some other invertebrates are hermaphrodites, meaning they have both male and female sex organs. When they mate, they exchange sperm. Each fertilises the other.

More complex organisms are either male or female. The male sex cell, or sperm, must mix with the female sex cell, or ovum, to form an embryo. Corals rely on water to do this for them. They release their eggs and sperm into the water and enough eggs get fertilised to continue the population.

Frogs, some fish and some other organisms practise external fertilisation. The female lays her eggs and the male sprays them with sperm, fertilising most of them.

Most complex animals including some fish, most reptiles, birds and mammals, use internal fertilisation. The male places his sperm inside the female's reproductive tract where they fertilise her egg or eggs. The most common way of doing this is copulation. Basically, the male has a penis or similar organ which he places inside the female to deliver his sperm directly into her reproductive tract.