Depending on how your soba are served, the way of eating differs:
Soba served in a soup (usually the hot ones) are enjoyed by using your chopsticks to lead the noodles into your mouth while making a slurping sound. The slurping enhances the flavors and helps cool down the hot noodles as they enter your mouth. The broth is drunk directly from the bowl, eliminating the need for a spoon. It is not considered rude to leave some unfinished soup in the bowl at the end of the meal.
For soba that are served with a dipping sauce (usually the cold ones), there are a few more steps before you can enjoy them. First, mix some of the green onions and wasabi into the dipping sauce. Then take a few strands of soba noodles and dip them into the sauce before eating them.
If your soba were served with a dipping sauce, some soba restaurants will give you a little teapot (see photo to the right) towards the end of the meal that is filled with what looks like hot cloudy water. This is sobayu, the water that the soba noodles were cooked in. Sobayu is meant to be poured into your remaining dipping sauce after you have finished your noodles. This is how you can finish your dipping sauce by drinking this mixture and adjusting the amount of sobayu as you prefer.