Which energy saving light bulb...

Lamp maximum wattage is based on amperage, and probably heat output, although with non-halogen bulbs that's not so much a problem.

So as long as the actual wattage of the bulb (not the equivalent lumen output) is less than 40watts, you'll be fine

(Oh: In other words, your 20 watt bulb will be fine in the 40 watt maximum)

I use a 60w ESLB in my 60w lamp (for more light). I've had no problems.

Can someone explain how you know if you are using an energy saving light bulb? Are they flourescent? Something else? What makes them energy saving?

The most common "energy saving lights" are compact florescent and they generally have a curly cue look: http://en.wikipedia.org/wiki/Image:Compact-Flourescent-Bulb.jpg

They are energy saving because instead of the very inefficient process of electricity traveling through a thin filament (which loses a lot of heat... I think around 90% of normal incandescent light bulb energy goes to heat), they excite certain gases, which then emit light. Because of this different design they use much less energy (about 75% less), and last much longer (about 10 times).