Negative Double
Because we open such light hands, it's not a good idea to play negative doubles as high as some other players prefer.  Our negative double is only as high as 3

Responsive Double
An example may be best.  If my partner doubles an opening bid of 1 I know he has a 4-card spade suit and support for a minor.  If the next opponent raise to 2 and I'm not interested in my partner's spade suit I can use a Responsive Double.

In general, a Responsive Double tells my partner I am not interested in the suit he is known to have, and I would prefer that he choose his best second suit, in this example a minor.  It's important to remember that the opponents must bid and raise the same suit.  If we double a new suit by the partner of the opening bidder, that's a penalty double.

Support Double
I don't know why the ACBL says this bid is alertable when the Responsive Double is not.
I think this agreement works much better with other bidding systems, especially when the heart suit is involved.  Anyway, if I open the bidding 1 and my partner responds with a major suit then I can use this convention to show 3-card support when the next hand interferes.  A double or redouble indicates 3-card support while an immediate raise shows 4-card support.

The problem is that we sometimes respond to 1 with a 3-card heart suit.  I doubt we should be using Support Doubles after a heart response, but so far it hasn't created a disaster.  (When it does, we will probably change this.)

DOPI
This is a special double used when partner opens 1 and the opponents overcall.  It's a method of conveying how many controls responder is holding.  The DOPI acronym is in two parts:  DO means Double with Zero while PI means Pass with One.  Bidding the next ranking suit is an artificial step response showing two controls, etc.

We use this method in another sequence, too.  When one of us opens a major and the other responds with a simple raise which is game forcing, we use DOPI if the next hand makes an interference bid.