The Blades are the Emperor's elite espionage, military, and diplomacy service, a prestigious service order for citizens who demonstrate the greatest loyalty to the Emperor. To be named to the Blades by the Emperor is a great honor, and publicly acknowledged members serve openly in noble courts and diplomatic posts. Privately, many Blades members act as the Empire's intelligence agency. Such agents conceal themselves with secret identities, operating in disguise as couriers, observers, and spies throughout the Empire. As the Emperor's hidden eyes and ears in the provinces, they watch the Emperor's enemies, look for opportunities, make reports, and act on the Emperor's command.
To join the Blades you must go to Balmora and talk to Caius Cosades. To find him go to the South Wall Cornerclub and ask around. Doing the Blades quests starts you out on the MorrowindMain Quest. The only person who gives you Blades quests is Caius Cosades, who is in charge on Vvardenfell. If you kill anyone related to this faction you will not be able to complete the Main Quest or, subsequently, finish the game in the expected manner.
Unlike with other factions you will not be able to rise through the ranks and lead the Blades. After the Main Quest (and since Caius Cosades is leaving at some point) you will be stuck at rank 5 as an Operative. Of course, as Caius points out, you, as an Operative, are the highest ranking Blade in Vvardenfell. All promotions are given through the quests, and don't actually check skill and attribute requirements.