What's the rule about changing hands during an at-bat?

The video:
http://www.bugsandcranks.com/the-clubhouse/switch-hitter-vs-switch-pitcher/

In college:
k. Pitch both right-handed and left-handed to the same batter during a plate appearance (ambidextrous-pitcher rule).

A.R. 1 — When facing a switch hitter, an ambidextrous pitcher shall declare the hand with which to pitch to the hitter.

That's the only time the phrase switch hitter appears in the 2008 rulebook, so I'd assume they can switch as much as they want.

MLB:
Nothing that I found.

[This message has been edited by mtp2007 (edited 6/20/2008 6:51p).]

The pitcher must delcare which arm is his throwing arm for the batter. The batter then chooses which side of the plate to swing from.

Just like any other situation, if the pitcher is taken out, the batter can switch sides according to the new pitcher.

I've always wondered, how exactly would a switch pitcher work? does he have two gloves at the mound? he can't go to the dugout and switch gloves, nor can a coach bring a different glove out to him.

A double palmed glove?

It's a double-thumbed glove, and they cost a small fortune.

Not a very good pic: http://www.nytimes.com/2007/04/06/sports/baseball/06pitcher.html?_r=1&oref=slogin

Better pic:



PS - I did a GIS of "switch pitcher" and found this picture:

Thanks for the answers, and thanks to AggieBand for making it Aggie related.