You won't always have this option, but if you do have twenty minutes to put together a two minute speech, use it. You won't be sorry.
Jokes that will work with twenty-somethings may only give you crickets with a crowd of retirees, and might not resonate with thirteen-year-olds either. Plan accordingly, again, if possible.
Always. Thank whomever asked you to speak and also the person/entity putting on the event (if they aren't one in the same). Introduce yourself and state why you are there.
People like to feel that they have a personal connection, and hearing stories that actually happened is an outstanding way of making that connection in their brains. Even though they might not have been there at the time of the "incident," they will feel included because you chose to share the story with them.
It looks good on everyone. Don't forget to pack some into your speech. In my case, I tried to make my mention of myself a minimum in my speech because I was not there because of something I did, I was there for the bride and groom.
Everyone loves a laugh, and you will seem less dry and more approachable if you can fit one in.
These are best done when you have some time to find a good one. If one is included, it is typically at the start and sets the tone and subject for the speech. I chose to end with one that fit nicely with my toast. Also, make sure that you know who actually said the quote, as there are some famous ones that are often mis-attributed.