India is a socially conservative country, and some Western habits can be perceived as dishonorable for a woman in much of the country, though India is coming out of its conservative image rather quickly, especially in big cities.
Outside of the larger cities, it is unusual for people of the opposite sex to touch each other in public. Even couples (married or otherwise) refrain from public displays of affection. Therefore, it is advised that you do not shake hands with a person of the opposite sex unless the other person extends his/her hand first. The greeting by a Hindu is to bring their palms together in front of their chest, or simply saying Namaste or Namaskar. Both forms are equally polite and correct, if a little formal. Almost all the people (even if they don't know English) do understand a "Hi" or a "Hello". In most parts of northern India and cities, it is quite acceptable to offer a "Hello" or "Good Day" followed by a handshake, regardless of gender.
Outside of trendy places or high society, women generally do not smoke. In some rural or tribal areas women do smoke, but discreetly.
Places such as Discos/Dance clubs are less-conservative areas. It is good to leave your things at a hotel and head down there for a drink and some light conversation. Only carry as much change as you think you would require since losing your wallet or passport means that you will waste a considerable time trying to get any kind of help in that regard.
People are generally modestly clothed even at the beaches, so be sure to find out what the appropriate attire is for the beach you are visiting. In rare places like Goa, where the visitors to beach are predominantly foreigners, it is permissible to wear bikinis on the beach but it is still offensive to go about dressed in bikini on the road. There are a few beaches where women (mostly foreigners) sunbathe topless but make sure that it is safe and accepted before you do so.
It's not so safe to walk in isolated places if you are a solo female traveller. Sex crimes against tourists occur in some tourist spots. At night, never walk on the street or take a taxi or auto-rickshaw with clothes such as tight shorts, a miniskirt, sports bra, tank-top, or other clothes which expose a lot of skin. If at all possible, refrain from areas that other tourists avoid.
In local/suburban trains, there are usually cars reserved only for women and designated as such on their front. In Delhi Metro trains, it is the first compartment.
In most buses (private and public) a few seats at the front or at one side of the bus are reserved for women. Usually these seats will be occupied by men and, very often, they vacate the place when a female stands near gesturing her intention to sit there. In many parts of the country, women will not share a seat with a man other than her spouse. If you sit near a man, he may stand up from the seat and give his seat also to you; this is a sign of respect, NOT rudeness.
Street parties for holidays are usually filled with crowds of inebriated men. During festivals such as Holi, New Year's Eve, and even Christmas Eve, women can be subjected to groping and sexually aggressive behaviour from these crowds. At such time, just scream or make a scene pointing your finger at the person. People will come to your help. It is less advisable for women to attend these festivities alone.
Friendly conversation with men you meet on trains is sometimes confused by them with flirtation. In some scenarios, this can lead to unexpected sexual advances; this happens to Indian women as well as Westerners. Befriending Indian women, however, can be a wonderful experience for female travellers, though you might have to initiate conversation. An easy topic to get things going is to talk about clothes, food.
It's not disrespectful for a woman to tell a man eager to talk to her that she doesn't want to talk - so if a man's behaviour makes you uncomfortable, say so firmly. If he doesn't seem to get the hint, quietly excusing yourself is a better answer than confrontation.
Dressing in traditional Indian clothes, such as salwaar kameez (comfortable) or saree (more formal and difficult to wear) will often garner Western women more respect in the eyes of locals.The idea is to portray yourself as a normal person, instead of a distanced tourist. Easy clothing is to wear a kurta paired up with your regular jeans or a salwar. They are very comfortable and most of the women do the same.
"Eve Teasing" is the most common term used in Indian English to refer to anything from unwanted verbal advances to physical sexual assault. The simplest way to avoid this remains the same as in your home country. Anything overt should be treated in a firm manner and if needed, ask the local populace (women in particular) to try and get the message across. Avoid confrontation if at all possible. Sticking to such area is not recommended.
While hospitality is important in India, it is not common to see people offering to share food or cookies while they eat. Some such offers are genuine and some not. In case you are travelling in train, you are offered food from a big and rich family type group, you can take a bite. But if you are offered something by men or even a couple eating a part of it, try avoiding it, as the other part may have sedatives (this may be so that they may loot your belongings when you become unconscious). You can reply with politeness and say no with a smile; they won't mind or take it personal.
Be careful while going for a body-massage.
Body checking (such as at airport) by police/security officer of the opposite sex is not allowed in India.
In line with increasing of sexual assaults, Tourism Minister has suggested female tourist not to go alone in the night and avoid using mini skirt or even knee length dress.