Ok, squirrel, let me see if I can do a summary for you of what's been posted thus far.
1. The Cartel and the Tribes may be taken as allies by any Corp, unless that Corp specifically lists otherwise (Imperial, for example, cannot take Inheritors as allies).
2. Any other units available as allies will be listed at the beginning of the appropriate army list (House Sagielli, for example, is allowed Brotherhood Dedicated units as allies, except named personalities).
3. Allies count as a Support choice in army construction, so you must have 2 Grunt units from your original army to field an allied unit.
4. All Grunt/Elite/Individual buying criteria for both your original force and allies must remain legal. So, say you wanted to take 2 allied squads, one grunt, and one elite. You would need 4 grunt squads of your original house to do this. The 4 squads gets you two support choices, so those are legal, and you have to take an allied grunt to get an allied elite, since every force has a 1:1 grunt/elite ratio. You could also take 1 grunt ally, and 1 individual ally, if you chose to.
Hope this helps.