The wattage of a bulb is the amount of energy it puts out per second. So a 60 watt bulb gives out 60 joules of energy out per second. If you wanted to check how much power (wattage) a bulb is using you could put a power meter where you plug in the lamp with bulb and measure the power there.
You could also, but it is a little harder, measure the wattage of the bulb by measure the amount of heat and light energy coming from the bulb using temperature and light sensors.
BUT and because I’m really an engineer and not a scientist. The wattage is written on every bulb, just read it and then make a cup of tea with all the time you saved 🙂
As a cheap experiment, you could probably estimate the wattage by trying batteries of different sizes. The voltage and maximum current a battery can provide should be labeled on them. So if you try hooking up batteries to the light bulb in order from small to large, you should end up trying a larger battery that doesn’t make the light bulb any brighter. Then calculate the watts being used by the lightbulb by multiplying the voltage by the current labeled on the battery. I haven’t tried this myself, but it might be a fun experiment- but get adult supervision!