I'm not an engineer professionally but I'm interested in. So my question is, how to recognise the wattage of a resister? And how to measure it using multimeter?
You cannot measure the wattage of a resistor with a meter. It is a function of its mechanical properties alone, how much heat it can dissipate, what temperature it must stay below.
Until you have some experience looking at resistors and saying 'oooo, that's about 0.1 watts for a chip resistor this small, or about 10 watts for a wire-wound, metal cased, heat-sunk resistor about that big', you must read the data sheet for the resistor, or the description on the site you're buying it from.
You must exercise care when trying to compare an unknown resistor in your hand to a picture on a data sheet. It's better than nothing, but maximum permissible temperature depends on the materials used as well, so it's not 100% foolproof. Any resistors you buy, keep them identifiable. Any random ones you get, guess what type it is from data sheet pictures, and then work to half that power for safety.
You could alternatively fit a thermometer to it, decide a permissible temperature rise, then gradually increase the power you supply to it until it reaches your permissible temperature.
Be aware that the headline figure for power is usually for an isolated resistor in a 25C ambient, so you need to read the data sheet for real world applications. If you are building commercial equipment, you will probaly derate the power they suggest further to allow for extra reliability.
Be aware that in some fonts, the character \$\Omega\$ is erroneously rendered as W (I've seen this painful error on so many supplier sites)