Do you need two hands to cast a spell? It only says "you must be able to gesture."
I don't know the reference of the quote, but for AD&D:
Only 1 hand and arm are needed to cast a spell unless the spell states otherwise.
Think of this like 4E implements. The resource is your PCs arms. One must be free to cast. Material components are the default price, so they are disarm-able like a weapon. Of course, some spells do away with one or both of these. There were no spells I know of, which had no verbal component. Those are also a drawback in a round, more so than needing to hold a weapon (2hd weapons offering more payoff because both hands were required to use).
Bards can use shields. Can my bard cast his spells while holding a shield in one hand? His other hand will be free.
Bards were prestige classes requiring at least 5 levels of Fighting Man or Fighter. So yes, bards are trained in shields. Anyone can use a shield untrained.
Like a M-U, Bards can cast most spells with one hand and arm when somatic components are required. The other hand and arm can be used for other actions. Standard shields require a hand and arm to use. But other shield types require more and some less.
Alternately, what about casting a spell while both hands are holding something? Do you need the entire hand free to gesture?
You need the entire arm and hand free to gesture. Armor interferes with this to a degree. Like any kind of interference there's a chance for spell failure. This, of course, excludes spells without somatic components.
Unless this is a non-somatic spell, you cannot cast a spell while both hands or arms are otherwise occupied.
This goes with brain activity too. Maybe some speech is possible, but concentration is required to spellcast. For some hardcore players this means they won't converse that round with other players.