Alice: Nomimono wa nani ni shimasu ka? (what do you want to drink?)
Kenji: Sou desu ne. Ocha ni shimasu. Alice-san wa? (I think I'll have tea. What about you?)
Alice: Watashi mo ocha ni shimasu. (I'll have tea, too.)
Among friends, when deciding what to order at a restaurant, it is appropriate to use the ~ni shimasu to ask questions. Rather than asking "Nani o tabetai ka?" (What do you want to eat?) You would typically ask "Tabemono wa nani ni shimasu ka?"
When ordering, though, you would use ~o kudasai, or ~onegai shimasu.
Alice: Sumimasen! (Excuse me!)
Waiter: Hai? Gochisousama? (Yes, what would you like?)
Alice: Ocha o futatsu onegai shimasu. (Two teas, please.)
Waiter: Yorokonde! (With pleasure!)