Alliance Navy/Marines Ranks:

Serviceman 3rd Class / Private 2nd Class
Serviceman 2nd Class / Private 1st Class
Serviceman 1st Class / Corporal

NCOs

Service Chief
Gunnery Chief
Operations Chief

Officers

2nd Lieutenant
1st Lieutenant
Staff Lieutenant
Lieutenant Commander
Staff Commander
Captain / Major
Read Admiral / General
Admiral
Fleet Admiral

Military Regulation:

If your superior is not an officer (they would be considered an NCO, or non-commissioned officer) then you do not refer to them as 'sir'. You refer to them as their rank, or suggested nickname. An officer, if not known, is considered any rank at or above 2nd Lieutenant. An officer, on the other hand, is referred to as 'sir'.

Any time seeing an officer that is a higher rank than you, regardless of race, it is important to salute. You must also comply to orders given by the higher ranked officer. This rule is void if the officer's orders conflict with that of an officer belonging to your own race:

If a Turian Captain tells you to only return fire, and you're Human, you comply with the orders given. If your Alliance Lieutenant gives you an order to fire on sight, you would listen to your fellow Human, because he has immediate command.

Each rank normally has some form of leadership. Leadership roles are as follows:

Servicemen: are the butt end of the military, rarely have command, except a first class serviceman. A Serviceman 1st Class can have command over a small firing squad, in cases where an NCO is not available.

NCOs: traditionally lead squads into battle. Most squads consist of five or six good men and women. Sergeants are often working their way up to be a Commissioned Officer, and are seen as respected leaders of small groups.

Officers: lead large groups of men and women. Lieutenants lead platoons, or groups of 30 people, Captains (often known as COs when they lead Companies) lead Companies, or groups of around 100 people, Lieutenant Commanders will often lead single ships, which can contain hundreds of people. Colonels, referred to as Captains in the Navy, also control ships, much like Commanders do. All of the Admiral rankings command different amounts of people, but, for the most part, command at least one thousand troops, and fleets of ships.

Update: Alliance Space Command Ranks

Enlisted
Airman
Airman 1st Class
Senior Airman

Non-Commissioned Officers
Staff Sergeant
Technical Sergeant
Master Sergeant

Officers
Staff Lieutenant
Flight Lieutenant
Captain
Major
Lieutenant Colonel
Colonel
Lieutenant General
General
Star Marshall