Depending on the script, you might also be able to run it by highlighting its contents in a text editor, then click-dragging it into one of your viewports.
Also, start looking over the 'MEL and Expressions' section in the manual. You should start learning about that scripts folder Keith mentioned, the Script Editor window, the Expression Editor, and so on.
MEL Scripts are different in terms of the way you should execute them. The best way is referring to its instruction text or pdf which is coming with the script, or if you don't have any you may open the mel file with a note pad in your windows and read the head part of it, usually the programmer mentioned the method of running the script in there. Anyway if non of the advises helped, one simple way which might be useful sometimes is, opening the Script Editor and go to File > Load Script and simply browse the mel file in there.