In Apple’s Mail on OS X 10.4, there are two apparent ways to search by e-mail address: you can either type the e-mail address into the search box (which means, obviously, you need to know the e-mail address), or you can copy the e-mail address field from any one message, then paste it into the search field.
But here’s a third method, and I think it’s by far the easiest and fastest way to search by e-mail address: just drag any message from that e-mail address into the search box (drag it from the message list panel). When you do, Mail will automatically extract the e-mail address and show it in the search box—and automatically start the search as soon as you release the mouse button. It doesn’t get much quicker or easier than that.
Note that this is not necessarily a search for e-mails from the chosen e-mail address—Mail remembers which settings you last used when searching (i.e. to search the entire message, or the From, To, or Subject fields). So when the results appear, take a quick look at the type of search that ran, and then click one of the other buttons if that’s not the specific type of search you wanted to use.