Ok, a player starts out with a level of Ranger, and then heads to Barbarian for level after level.
So at what point does the character start getting two attacks per round.
At: Rgr1/Bar5 (6 levels total so +6/+1, +1 from ranger +5 for barbarian and second attack based on idea that normall when your first bonus hits 6 you get a second attack at the bonus of the first minus 5)
Or: Rgr1/Bar6 (7 levels, So rgr still +1 and now barbarian is at +6/+1 so that total bonuses are +7/+1)
This is clearly not including str, des or any feat modifiers.
When his BAB reaches +6, like everything else.
You get extra attacks whenever you can subtract 5 from your weakest attack and have the result be at least +1. So +6, +11, and +16 total BAB. A Barb 5/Oracle 1 would only have +5, so wouldn't, but your Barb 5 / Ranger 1 would have a +6, so would.
The BAB gained from all classes adds together if you multiclass. You need a total of +6 BAB to gain another attack. This number is unmodified by STR, DEX or anything else. Thus, it is called your Base Attack Bonus.
In your case, the attack would be gained at 1 Ranger/5 Barbarian because these classes each gain 1 BAB per level.
When you add in other classes (as Bobson described above), you get different results. In his example, the character would need 5 Barbarian/2 Oracle to achieve a +6 BAB and gain the extra attack. This is because the oracle gains BAB at a different rate from a Barbarian or Ranger.