At a typical Chinese restaurant the default place setting will include chopsticks, a spoon, and a bowl for soup (or temporary food storage). Place settings in upscale restaurants often include small dipping bowl with vinegar and soy sauce. If you're looking for a fork and knife, you will probably find yourself out of luck, unless you are in a 5 star hotel, or high-end restaurant.

wan2 bowl
盘子 pan2 zi3 plate
筷子 kuai4 zi3 chopsticks
调羹,汤匙, 勺子 tiao2 geng1, tang1 chi2, shao2 zi3 spoon (usage of these 3 words differs by region)
叉子 cha1 zi3 fork
刀子 dao1 zi3 knife
杯子 bei1 zi3 glass
一口杯 yi1 kou3 bei3 shot glass
纸巾,餐巾纸 zhi3 jin1, can1 jin1 zhi3 napkins/tissues
烟灰缸 yan1 hui1 gang1 ashtray
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