multiplication equivalent of the summation symbol

It's a capital pi (for product): $\prod$. You can sometimes find useful symbols and guess what they mean from their $\LaTeX$ names, although I guess the most reliable way to find useful, well-known symbols is just to read a lot of math.

I google "latex symbols" when I need something I can't recall. That'll give you many lists and tips. For example, if you choose the first hit, the AoPS list and look for the sum symbol you'll find the product symbol right below it. This is but a simple example of a general technique of exploiting organization and classification on the web to discover information about similar items.

For the inverse, when you know the symbol but not the name there is deTeXify which let's you draw the symbol and does OCR to find the name. For deeper questions there's the (La)Tex SE site.