Always remove your shoes, socks and hat and wear long trousers and long sleeves prior to entering a Mosque, or Temple in Singapore.  

Women entering a mosque must wear a long cloak and head-covering, which are usually provided at mosques for the purpose. Non-Muslims may not enter a Mosque during times of prayer. Footwear should also be removed before entering a Singaporean home. 

Owing to the multicultural diversity in Singapore, the type of greeting may depend on ethnicity. The handshake is widely recognised as the main greeting. However, it is not generally acceptable Malay women to shake hands with a man, though she may with another woman. The proper form for a man to greet a Malay woman is to place his hand on his heart and bow slightly. 

In Chinese culture, handshakes are light, and it is acceptable for a man to shake hands with a woman, but the protocol is for the woman to offer her hand first. Indians normally handshake only with their own sex, and a smiling nod is the acceptable greeting between sexes. 

Never point. If you need to attract attention, motion with the palm of your hand. Never touch anyone on the head. It is a common gesture in many societies to affectionately ruffle the hair of children, but the head is considered sacred in Asian cultures and such gestures will not have the intended effect. 

Overt public displays of affection between couples is frowned upon, particularly in traditional areas, and shows disrespect to the native culture. As male homosexuality is still technically illegal in Singapore, gay men should exercise caution in this regard. 

Tipping for services in Singapore is not mandatory and in general unnecessary, but will be accepted by Taxi drivers, tour guides, restaurant and hotel staff.  

When dining among the Malays, eating with the hand is common and care should be taken to use only the right hand and never the left, which is considered unclean. Never lick your fingers afterwards. If eating with a fork and spoon, the fork is used for prodding and manipulating food on the plate but eating should be performed with the spoon.  

If dining among Chinese, Chopsticks should be used only for eating and never employed as a means of gesturing, drumming or placing in your hair. When you have finished your meal place the implements together level across the top rather than leaning into the bowl, and on no account leave the chopsticks pointing straight up as this is traditionally interpreted as either obscene or even a curse or omen of death. 

It is not the practise anywhere in Asia, especially for women, to touch a monk, or even their robes.