Reprinted with permission from Countess Dulcia MacPherson, OL, OR
Etiquette rule for titles is that you used the highest title the person has. Period. If you want or need to include other ranks or awards in the introduction, you include them AFTER the person's name. Title stacking is incorrect, both in period and in the modern world and just sounds goofy anyway. We hear it done incorrectly in the SCA so much that folks are used to the way it sounds and tend to think that it is correct, but when in doubt, try transferring SCA practices to the modern world. For example, Dwight D. Eisenhower: He is referred to as "President Eisenhower"... not "President General Eisenhower" which is the modern world equivalent of saying "His Majesty, Sir Stick Jock".
Or to use a more analogous example - Prince Charles: If we used the SCA style of (incorrect) title stacking he would be: "Prince, Prince, Duke, Duke, Earl, Earl, Knight, Knight, Baron, Lord Charles". While it gets all his titles into the mix, it also doesn't really tell you anything much and sounds pretty stupid. If, for whatever reason (really formal introduction, heralding someone into a tournament, whatever) you wanted to use all of his titles you would say: "Prince Charles, By the Grace of God Prince of Wales and Scotland, Duke of Rothesay, Duke of Cornwall, Earl of Chester, Earl of Carrick, Knight of the Garter, Knight of the Thistle, Baron Renfrew, Lord of the Isles, Great Steward of Scotland and Companion of the Order of Merit." That's actually the format that is used today and should be used in the SCA as well.
So instead of "Duke Sir Big Shot" you might say
"Duke Big Shot, Knight of the SCA, Companion of the Order of the Fuzzy
of the Barony of Nowhereville, Protector of small furry creatures and drainer
of many kegs of beer", which is a LOT more entertaining, provides more
useful information about him to those who didn't know much about it and is more
period correct. But in an introduction, you simply say "Duke Big
Shot" if that's all you know about him, or maybe "Duke Bigshot, who
has a soft spot for small furry creatures".
Introductions are unique in that you are introducing people for a reason and your introduction should encompass that reason. If you are introducing someone to someone who may be able to help them in some way (teach them to fight, teach them costuming, sponsor them in entering a tournament or contest, or whatever else) you should include that information in the introduction - "Countess Dulcia, may I present Lord Rapier Dude from my group who would like very much to participate in the Order of the Rose Lyste, if you are not already sponsoring a fighter." If the purpose of the introduction is to introduce people you like to each other it might be "Lord Good Times, may I present my best friend, Eddie? This is his first event but I've told him so much about the fun we've had together that he wanted to meet you and hear your story about the road trip to Pennsic for himself." If the purpose of the introduction is simply to expose someone to people you consider important to the group/kingdom/SCA, then all you need to do is say "Your Majesty, may I present my sister Jill?" However, if you want them to have something to chat about for a moment, I would suggest adding something of a personal nature to the introduction.