There's a few different things going on here, so I'll go through them in order.
Standard Action Attack
If you use a standard action to attack, you get one attack at your highest base attack bonus. It doesn't matter how many weapons you are holding, or which hand they're in. You can pick the one you want to use for this attack.
Full Round Action Attack
If you use a full round action to attack, you can get extra attacks. Those extra attacks occur at BAB +6, +11, and +16 for a Fighter. Each extra one is -5 from the previous one.
So a level 6 fighter has 6/1, and on a full attack action gets two attacks. The first is using BAB +6, the second +1. At level 11, it would be +11/6/1. These are shown in the detail for each class in the Players Handbook, here is the Fighter one.
If you happen to be holding two weapons, you can use either, or both of them, for those two attacks. If our level 6 Fighter is holding a Shortsword and a Dagger, he gets to roll two attacks. He can do both with one weapon, or one with each weapon. This is not considered Two Weapon Fighting in the rules.
Full Round Attack with Two Weapon Fighting
In this case, you are explicitly using Two Weapon Fighting. You still get the attacks you would get for a full attack, except you need to pick a "main hand" weapon during the action and all those attacks use that weapon.
In addition, you get one additional attack at your highest base attack bonus, with your second weapon (the "off hand" weapon). All attacks in the round take a penalty, which depends on if you have the Two Weapon Fighting feat and the weapon category of your offhand. If you have the feat and a light weapon in your off hand, the penalty is -2.
You only get one offhand attack no matter what your BAB is. The feats Improved Two Weapon Fighting and Greater Two Weapon Fighting grant you additional off hand attacks.
So your example fighter with BAB +7/2 would on a full round attack get two attacks with his main hand, one attack with his off hand, and an additional attack with his off hand if he has the Improved Two Weapon fighting feat. Total of four attacks. Those attacks would be at BAB +5/0 and +5/0, due to the -2 penalty for two weapon fighting.
Note that characters, in the rules, do not have a "main hand" outside of this specific case. That means you don't always have to pick the same hand or the same weapon to use as your "main hand".
You didn't ask this specifically, but to avoid confusing you later - natural weapons (claws, bites, and such) don't work the same way. Those do not get additional attacks from BAB. Monsters as they get more powerful just get more natural attacks, and they can use all of them at once with a full round attack.
The monster's attack entry in the Monster Manual or SRD has these things factored in already, so if you follow those you will be fine. :)
Yes, it slows things down
Two weapon fighters (like Rogues) can very quickly get to several attacks, and that means a lot of rolling. It does slow things down. Once you understand how it works it slows things down less than when it's new, but it can make combat slow. If you hit with those rolls you'll also get multiple damage rolls to work out as well. If you have different colors of dice, you can roll all the attacks
(and damage) simultaneously, which can make it move a bit faster.
It's useful for the DM to know the armor class of the enemy being attacked, so when the fighter rolls you know quickly if it's a hit or not. For the fighter, his character sheet should list his multiple attacks with the math for their rolls already done, so he can just look at his sheet and know "oh my second attack is at +3" rather than having to do the math every time.
It's also worth noting that those attacks don't have to be against the same target. If you kill something with your first attack in a full attack and another enemy is in range, you can switch to attacking that enemy with your remaining attacks. You can't move to do that, so they have to already be in range.