I was wondering how the "diplomatic pouch" works. I understand it is a
general agreement that packages to embassies overseas are not checked
by the host country, but I would like some detail about the rules and
how they are used.

Well ... MI5 certainly examined every Diplomatic Pouch that they could
get their hands on during WW2 ...

This is no expert's opinion.  "Diplomatic pouches" which includes all
shipments to and from and under the auspicize of a foreign
embassy/consulate are not subject to customs controls. However, not
just anything can be shipped by this way.  Misuse, drugs and weapons
will probably be identified, the shipment detained and an
international "discussion" result.

Here are a couple of websites that apply:

http://foia.state.gov/masterdocs/05fam/05m0330.pdf

http://www.mfa.go.th/web/110.php

One of my Diplomatic friends (British) told me that he was in a Middle
Eastern country where alcohol was and is forbidden.

On one occasion, the incoming 'Diplomatic Pouch' (which was actually a
crate) was accidentally dropped by the ground staff at the airport and
- Guess what? - alcohol poured out everywhere!

Now, what do you make of that?

And BRitish or US diplomat in Leningrad or Moscow were said to have
sent their shirts by pouch to Helsinki for laundring.  Pouch is a
general word, not just a mail sack or a briefcase handcuffed to a
courier.  Larger diplomatic shipment -Freight - will be accompanied by
a courier to assure that the diplomatic status is respected and to
have someone immediately available to decide what to do if there is a
delay for other reasons (What to do with flowers for Madame
Ambassador's party ;)