When discussing lighting, it's important to remember that watts are a measure of electrical power, and lumens are a measure of usable light output. So, when you talk about watts of a light bulb, you're asking how much electrical power it uses. Usually, for a light bulb, you're really concerned with how much light it puts out, which is measured in lumens. To compare different light sources, you can put both of those numbers together to create a number called the efficacy. Efficacy is measured in lumens per watt, and it's a measure of how well a lamp converts electricity to light.
Look up the light output and calculate the efficacy of the incandescent bulb you wish to compare. For example, take a 60-watt incandescent bulb --- the most common bulb for consumers in the U.S. On the EnergyStar "Learn About Light Output" website you will find that this bulb puts out 800 lumens, so the efficacy is 800/60 lumens per watt, which is about 13 lumens per Watt.
Find the light output and electrical power usage of the LED bulb. Data on qualified LEDs can be found at the EnergyStar website. As a random example, Sylvania's LED8G25 uses 8.43 watts to produce 434.7 lumens. The efficacy is 52 lumens per watt.
Compare the electrical usage, the lumen output, and the efficacy of your selected incandescent bulb to your selected LED bulb. For the example, the comparison of the 60-watt incandescent to the LED is:
Electrical power usage: 60 Watts to 8.43 watts. Incandescent about 7x LED.
Light output: 800 lumens to 434.7 lumens. Incandescent about 1.8x LED.
Efficacy: 13 lumens per watt to 52 lumens per watt. Incandescent about 1/4x LED.
So, for this case, the LED uses only 1/7 as much power, is four times as efficient, and puts out a little more than half the light of the incandescent.