Use a chef's knife, or better yet, a julienne peeler, to slice the cucumber into long, skinny strips. Toss the super seedy inside strips. Then you can slice the remainder into 3-inch long strips (as shown) or leave them long.
Bring a large pot of salted water to boil and cook the soba noodles until al dente, according to package directions (do not overcook them!). Drain and rinse under cold water.