In general, different animals may mate in different manners, but in most cases the main purpose is to transfer sperm from the male to the female.
The mating process always involves the struggle of one sex (often the male) to win the mating with the female. The failure of this process is normally a few or no offspring to sustain the generation of their own species. In contrary, a successful male to attract the female of his species may assist in passing his genes on to the next generation. However, in the world of insects, the male may attract a completely different kind of female as his partner. The female insect is particularly more interested to lay her eggs rather than to look for sex.
In regards to mating, Lost in Arizona, a writer at Triond has a brilliantly written article entitled 10 Bizarre Mating Technique to supplement the incomplete part of this article.
The Indian Bullfrog: Ready and Call for a Sexual Service!

(Image source: REUTERS 2006-06-24)
The Indian bullfrog (Hoplobatrachus tigerinus) is the largest frog in Pakistan which is usually found hibernating by burrowing in soil during winter as well as during drought.

(Image source: REUTERS 2006-06-24)
During mating, the male (lemon yellow in color) will croak repeatedly to attract the attention of the female (dull and light-brown color). The croak of the male has a powerful nasal “Cronk, cronk, cronk”, but sometimes it sounds like “oong wang, oong wang, oong wang”. When the mating season begins, the males will repeat their aggressive croaks several times by sitting close to each other in the shallow water or pond, splashing into the water, jumping over each other to attract the females. At the same time, the female will lurk around by the calls of the males, initiate copulation by making contact with a carefully selected male. The males hang around the periphery, hoping to get lucky.

(Image source: REUTERS 2006-06-24)
If one of the males manage to grab the female frog they will jump in pair and somehow move together to a quiet place to avoid the fighting, pushing and tugging from other male frogs. There, the female will lay its eggs (2.5 to 2.8mm in diameter) in large volume with each of the egg enclosed with a layer of double coat of jelly.
Butterfly: Endurance beyond Love!

(Image source: Luis Romero, El Salvador [AP 2006-06-13])
The butterflies spend much time to search for mates. The adult males will usually search for the females of its own species which have the recognizable pattern and color in their wings. When the male spots his mate, he will fly closer; usually he is behind or above the female. Approaching closer and closer, the male will release the chemical substance called pheromones, while fluttering his wings more frequent that he usually does.

(Image source: Kang-Chae Lee, Korean Monthly Science Magazine “Science Dong-A”[Feb. 1996])

(Image source: Martin Kramer, Amsterdam)
To attract the female, the male make a special “courtship dance” which may consist of some peculiar dancing postures. If the female gets excited with his dancing, she may join him. There, they join their bodies together end to end at their abdomens. At this stage, the male passes the sperm to the female's egg-laying tube which will soon be fertilized by the sperm. The male is always unfortunate as he often has to face the death shortly after mating.
After mating ends, the female must go to select the correct plant species to lay her eggs. Once she is sure she has encountered her favorite plant, she will start laying eggs either as a single egg or in clusters which will be fertilized with the sperm that has been stored in her body while mating with the male. The produced eggs are enclosed with a sticky substance to enable the eggs to be attached firmly either on a stem or on the underside of a leaf.
Dolphin: You Guy All Crazy at Sex!


(Image source: SexyVixen)
Dolphins are by far animals that have strong sexual desires as they mate many times in a day. Nevertheless, each mating section ends very fast with on longer than 12 seconds. As the male dolphins have ravenous sexual appetites, they will always attempt to hump inanimate objects and even other animals like sea turtles. The male dolphin will often force the female to have sex. The other hushed-up fact is that the male has a retractable penis, the flaccid penis located within his body and both penises appear while on demand. Another cool fact to add in is that his penis is prehensile which can swivel to explore an object around him just like a hand.
My claps.