Here I am going to try and explain how the aliens breed, how they live and work. The information comes from the movies and from www.alien.com

The aliens are commonly called xenomorphs because of their many phases and different forms. Below I will go through the phases one by  one. The links from the headings lead to a pic of the phase in question.

Egg:

Eggs are created inside the alien Queen and exit through a tube from her extended abdomen
to stand upright on their own. This indicates that the eggs have definite "up" and "down" sides. The egg is approximately 2.5 feet tall with a leathery, translucent surface and is extremely flammable. It can survive for an indeterminate amount of time in various environments. For example: the derelict spacecraft on LV-426, the Atmosphere Processing Plant at the terraforming colony, and onboard the Sulaco. It is able to detect the proximity of
a potential host through sound and/or movement. The dormant egg then comes to life, with its top
opening like the petals of a flower and releasing the Facehugger.

Facehugger

The Facehugger is the parasite that hibernates inside the egg. When a host comes in close proximity to the egg, either through curiosity or by being cocooned, it triggers the parasite within to come to life and launch itself out of the egg at the potential host. It attaches itself by wrapping its tail around the victim's neck, causing him or her to gasp for air. It then firmly grasps the victim's head with its eight spider-like digits. Each digit has three knuckles. The Facehugger puts the victim in a comatose state and controls the amount of oxygen he or she receives by forcing a tube down his or her throat. Wind "bags" on the sides of the Facehugger pump air through the tube. It places an embryo within the host's chest cavity by using this same tube. After the embryo is planted, the Facehugger leaves the host's body and dies. The host soon regains consciousness with no recollection of the implantation process. The embryo develops quickly and eventually forces itself out of the host's chest, causing an extremely painful and violent death.
For protection, Facehuggers have concentrated acid for blood and will strangle the host with its tail if there is any attempt to remove it. It has an outer layer of protein poly-saccarides and can shed its cells and replace them with polarized silicon, which gives it a stronger resistance to harsh environmental conditions.
Facehuggers can use various species as their hosts (for example: the alien in the derelict craft, humans, and dogs) and can adapt to many different environments.
It has been speculated that the alien Queen originates from a "Super Facehugger," which is a larger, faster, and more heavily armored version of the parasite.

Chestburster:

The life of the mature alien begins when it bursts out of the host's chest, causing an extremely painful and violent death. At this stage, the snake-like Chestburster has a small cranium and tan colored skin. It is also extremely flammable, like the Egg. Chestbursters range from one to two feet tall.
After birth, the Chestburster will either feed on the remains of the host or seek shelter if threatened. It sheds its skin as it matures and the exoskeleton hardens and becomes darker. Its cranium also elongates.
The Chestburster on LV-426 had arms, unlike on the Nostromo. On Fiorina 161 it had both arms and legs and a noticeable inner jaw or tongue, giving it a more mature appearance immediately after its birth. It is speculated this is either because the alien actually inherits some genetic traits from the host as it develops, or because of varying periods of gestation which cause it to be at different levels of maturity when it is "born."
Incubation time also seems to vary. Kane, the victim from the Nostromo, had an incubation period of a few hours, while Queen embryo in Ripley matured over several days. It is believed that a Queen embryo will wait several weeks before emerging, allowing the host to travel and spread hives over a larger area.

Soldier:

The maturing Chestburster sheds it skin like a snake as it grows. Each shedding skin and increase of body mass may cause the secretion or loss of some of its acidic blood. Its exoskeleton hardens and grows darker while its cranium elongates. It develops sharp claws and a spiked tail. The tail is used for both balance and attack and has a stinger at the end. Spines on the alien's back provide protection for attacks from the rear. Mature aliens have concentrated acid for blood and a higher tolerance to fire than its earlier stages of life. The alien has two mouths, one inside the other -- the inner mouth being the alien's tongue. The tongue can extend up to one foot from the alien's mouth. Its strong driving force can easily puncture a human skull. It also does not appear to have eyes, which may mean it uses a form of sonar to determine its surroundings. The alien can be up to eight feet tall and is bi-pedal. The entire maturation process takes only a few hours. Because the aliens do not show up on infrared scanners, it is believed they do not emit heat. Soldiers are quick and agile with great strength, making them difficult to kill.
Like insects, Soldier aliens serve and protect their Queen, which is even larger and more dangerous. Some aliens will build and maintain the nest (Drones), while others will find and immobilize suitable hosts (Soldiers).
Although the aliens have a large cranium, it is believed they only have rudimentary intelligence. They know when to protect the Queen and her eggs, as on LV-426 when Ripley torches the eggs in the nest. And they were supposedly able to cut the power to the Operations Center. An alien also acted to protect Ripley on Fiorina 161 because she was carrying the Queen embryo.
On the Nostromo, it had six fingers and a smooth cranium unlike on LV-426 where they had three fingers and a ribbed cranium. On Fiorina 161, it tended to move around on all fours and ensured the unborn Queen was protected

Queen:

The Queen is born in a similar way to the Soldier alien, but her incubation period is longer -- several days instead of several hours. The cranium is much larger and flatter and the Queen is approximately two to three feet taller than the Soldier. Queens create and lay eggs through the use of their extended abdomen (Eggsac) and can survive for an undetermined amount of time without it. She has four arms, instead of the usual two.
The Queen, similar to a queen ant, is the only reproductive female in the hive and directs its operation, from its construction to the location of suitable hosts. It is believed that she communicates her will through the secretion of pheromones or possibly by an empathic link. She is more intelligent than the Soldiers and Drones.

Newborn:

A new, more dangerous breed of alien created as a byproduct of the genetic engineering by the scientists aboard the USM Auriga. The alien Queen retrieved from the clone of Lt. Ripley had a mixture of alien and human DNA, causing her to have a second reproductive cycle where she gave birth to this new alien breed. This alien/human hybrid believes that Ripley is it's mother.