Always remove your shoes and socks prior to entering a temple, monastery or home in Bhutan. Long trousers or skirts and long sleeves are the required attire when visiting religious sites. Photography is permitted only outside such buildings. 

Also be aware that it is considered rude to show the bottom of your feet toward religious objects or people in general, which can most easily be accomplished by sitting cross-legged. 

Although not mandatory, it is the tradition among the Bhutanese to leave a small donation when leaving a temple or monastery.

Handshaking as a greeting is not usual in Bhutan, though in modern areas it is becoming more of a feature in daily life. Traditional greeting takes the form of a bow with outstretched open hands palm upwards.

Never point at a person, or touch their heads. In general the people in Bhutan are not used to being touched by strangers, so tapping, hugging or putting your arm around someone is likely to regarded as a violation and cause unintended offence.

It is a common gesture in many societies to affectionately ruffle the hair of children, but the head is considered sacred in Bhutanese society and such gestures will not have the intended effect. If you need to attract attention, motion with the palm of your hand.

Avoid political comment and criticism, particularly of the monarchy.

Overt public displays of affection between couples is frowned upon, particularly in traditional areas, and shows disrespect to the native culture. Conservative dress, especially at religious sites, is recommended in public areas.

Tipping for services in Bhutan is discouraged by the Bhutanese government and is in general unnecessary, but will be accepted by tour guides.  

When dining in Bhutan, food is normally eaten by hand using only the right hand, as the left hand is considered unclean. When dining with locals, the host will ask the others to eat only after everyone has been served and will not serve themselves until everyone else has begun eating.