right-click on or next to button and select "inspect element"
find the html tag of the button. it is probably a <input type="button"> tag.
look for an onclick attrib on the tag, and copy the value of the attribute.
click the console tab of firebug and pase the code into the console.
click run, and the result should be the same as clicking the button.
if there is no onclick attrib, it's a little trickier.
you need an id for the input.
if it has one, great.
if not, while inspecting the input, right click the tag and select "new attribute", type "id" press enter and type "test1" and press enter.
click back on the console tab and type in $("test1").onclick.toString()
the code you need to run will appear in red text. copy it and paste it into a function, or run it from the console to simulate a click.