Here is some information about some of the major races involved with DS9.

Klingon: After the Khitomer Accords the Klingons became allies with the Federation. However recently the Klingons withdrew from the Accords when the Federation refused to back the Klingons invasion of Cardassia, but the Khitomer Accords were re-instated when the Federation and Klingons decided to work together to fight against the Dominion. Worf who is stationed on Deep Space Nine is the only Klingon in Starfleet.

Cardassian: The Cardassians occupied the planet Bajor for 50 years before leaving it with nothing. DS9 is the abandoned Cardassian station "Terok Nor". Recently the Cardassians under Gul Dukat joined the Dominion and are now at war with the Federation.

The Dominion: The Dominion are the main power in the Gamma Quadrant. There are many races in Dominion, many of which have not yet been encountered.

The Founders/Changlings: The Founders are shapeshifters and are the leaders of the Dominion. They are considered gods by all in the Dominion as very few have ever seen them. All their orders are given to the Vorta via subspace relay stations. Odo who is Chief of Security on DS9 is a Changling but chooses to live away from his people even though they want him to come home.

The Vorta: The Vorta are the only race with contact to the Founders. They basically control the Dominion. The control the drug Ketracel White which the Jem'Hadar need to survive and look after all contact with other races. All of the Vorta Field agents are clones so that if they are killed some way they can just be reproduced. They are also immune to most forms of poison.

The Jem'Hadar: The Jem'Hadar are the Soliders of the Dominion. They are Genetically engineered to fight, the obey The Founders and are addicted to Ketracel White to ensure their loyalty. The Jem'Hadar don't eat, don't sleep and there are no Jem'Hadar women.

The Ferengi: The Ferengi are the businessmen on the Alpha Quadrant. They have 285 Rules of Acquisition which guide their business deals.

More coming soon.