How do you say at your service in Japanese?

Rather than "at your service", Japanese people either greet their customers (I.E., "Irasshaimase!"/"Welcome!") or introduce themselves as the server (I.E., "Watashi ha anata no SAABAA desu"/"I am your server."

That said, the closest translation to what you want is probably: "Chuumon wo omachishiteimasu." This means, "I await your order." It is pronounced: choo-moan oh oh-mah-chee-shee-teh-ee-moss.