>pick up bowl with both hands
>hold bowl in left hand and pick up chopsticks with right hand
>lift bowl to mouth
>push solids in to mouth using chopsticks while the bowl is at your mouth
>stop drinking/eating and lower the bowl intermittently (don't need to put it down completely until you are done eating it or are having something else)
Things to avoid doing:
>leaning over your food
>picking out solids
>making a mess
>making loud noises
You don't have to fuss too much about picking it up with both hands or avoiding noise in informal contexts; then it is okay to be holding your chopsticks first, swapping between bowls in your left, and even to slurp a bit.
I'm sure there's some stuff I don't know or don't have quite right but you're not going to commit any major faux pas as long as you follow my advice.