An oshibori towel, in a wrapper or on a small tray, gives you a chance to wipe your hands (or even your face) before you begin the meal.
Except in Chinese restaurants that provide plastic chopsticks, you eat with wooden chopsticks that come in a paper wrapper. Take them out, split them in half, and hold the two halves in one hand with your thumb, forefinger and middle finger, as if holding two pencils. Then let the middle finger slip between the two sticks. One stick will rest between the forefinger and middle finger, the other between the middle and ring fingers. Watch how other people manipulate the sticks to figure out how to pick up pieces of food correctly.
To deal with soup, pick up the small bowl with one hand and sip from the edge of the bowl. You can dip your chopsticks into the soup to pick up small chunks of bean curd or thin slices of seaweed.
Noodles served on a wooden tray are simply picked up in bite-size portions. If served in a hot broth, alternate between picking them up and lifting the bowl to sip the broth. Slurping is a sign of a good appetite and eating with pleasure, and is in this instance, perfectly acceptable.