As the guy who wrote the search, I'm the logical candidate to explain the thing. I'm not quite sure what the other guys make of it, except that questions about it are bounced to me with remarkable alacrity.
Without further delay, I'll cut right to the subject: taming the vicious search ninjas. I mean, using the search engine. Same difference.
There are two main modes to the search. There's search, which displays a list of results, and find, which just takes you directly to a strip. Both are accessible from the index page. Hitting 'enter' or pushing the "go" button will initiate a normal search. Entering any text in the searchbox or checking any of the checkboxes will cause the find buttons to appear. They take you to the previous or next comic fitting the criteria you've provided. Or the search ninjas apologize for not being able to find anything, either way.
A brief note about the checkboxes - none checked is the same as all checked. It makes no difference, except that the latter may take slightly longer.
The search does a lot of interesting little things. One of the more useful ones is that if just put in a number and hit enter, you'll be taken to that strip. Go on, try it. I'll be here when you get back. One of the side-effects of this is that if you want to search for a number you have to enclose it in quotes, but that's the price of convenience.
The most important operator is the colon. It distinguishes between someone speaking and what's being said. The next most important operator is the asterisk: *. It's a wildcard, denoting that something goes there. There's a big difference between looking for Largo and looking for someone talking about Largo. Then there's looking for Erika talking about Largo, in which the colon makes a very big difference in the results you get.
There are a few useful magic words - note the highly technical term. One of them is "chapter". For illustration, here's Kimiko in Chapter 6. There's also "min" and "max", which do pretty much what you might expect. Just so we're clear, here's what Piro was up to between comics 400 and 500. There are other magic words, too. One of them is "meta", and it's how the checkboxes on the main page work. For example, here's the previous search, but limited to story comics only.
There's one deserving of special mention: "#:random". It takes you to a random strip within the criteria you specify. So if you're Alpicola, you can go to a random Megumi strip with ease.
For the more advanced user, there's also a subtraction operator: -. You use it by prepending it to a search term. It even works with magic words. For an example, here's Erika talking without Largo around. Furthermore, here's the same before chapter nine.
By popular demand, there is also a jump-by-date feature. Input a date in the "mm-dd-yyyy" or "yyyy-mm-dd" format, and you will be taken to the closest strip on or before that date. For example, this link takes you to the strip posted on March 28, 2007.
There may or may not be other functions. Explore as you will. Just watch out for the ninjas.