In the Jewish mourning tradition, mourners of the deceased will usually sit shiva. As someone close to the mouner or to the deceased, it is appropriate that you pay a shiva call.
A shiva call takes place usually in the mourner's home. The place where shiva will occur will be announced at the funeral. If you're unsure where the shiva house is and are uncomfortable asking the family directly, you can ask the funeral home as they should have this information.
Often before entering the shiva house, there will be some water and hand towels which you can use to purify your hands. Especially on the first day if coming from the cemetary, washing your hands is appropriate. When entering the house, you may notice a tall candle burning. Since shiva takes place for 7 days, these candles are designed to burn for 7 days and are often provided by the funeral home.
The mourners typically have the mirrors covered, may not wear make up or shave, and in general may not keep up with general daily grooming as they are not required to keep up external appearances while sitting shiva. Most people unless highly conservative will typically shower, brush teeth, and keep up with basic grooming however.
It's common for those in mourning during the shiva period to sit lower than everyone else. This is a sign of humility and being brought closer to the earth. Therefore, if you have the option of sitting on a couch or normal chair, leave the lower chairs for the mourners. In some shiva houses, there may be enough low chairs for everyone and if so you can feel comfortable to sit in one too.
As is typical for Jewish get-togethers, there is often quite a bit of food and drinks available. It is common for the friends and Jewish community to provide enough food for the mourners because they aren't epected to entertain guests or even to do their own cooking during the shiva period. The first meal upon returning from the cemetery is called in Hebrew the seudat ha'vra'ah, which means, "the meal of healing." As you arrive at the house, you should feel free to eat or drink as you wish.
Several times per day either a Rabbi or another member of the Jewish community will lead the people in the shiva house through the Mourner's Kaddish prayer.
You should feel comfortable to bring some food to leave at the shiva house. This is always appreciated and is better than bringing flowers or other types of gifts. Be sure to check if the shiva house is kosher and if yes, you should bring kosher food.
It's common that the mourners may not greet their guests and this is not considered rude. You're free to come into the shiva house, walk around and talk with whomever you wish. It's appropriate to greet the mourner with "I'm sorry for your loss" or "If there is anything I can do to help, please let me know". This is better than "How are you" as clearly they are not well emotionally.
In conversation, do not feel obliged to entertain the mourners. The period of shiva is dedicated to grieving and so if the mood in the house is solemn, that's ok. It is very appropriate to tell a story about the deceased or to share some memories. Sometimes there will be a photo album on the table and it's appropriate to look through it with or without the mourner with you.
Interestingly, a house of shiva usually has an air of a family gathering and doesn't feel so solemn. If someone makes a funny joke it's ok to laugh and in general enjoy the company around you, even if the occasion is solemn.
If you're not comfortable bringing food, another great gift is to make a donation to a charity that the deceased supported. For example, if they were close emotionally with Israel, you can plant a tree in Israel. If they were supporters of education, you can make a charitable contribution for that. Often at the funeral they will announce a charity that has been selected by the family.
Although the best way to show your support to the family in mourning is in person, it is also appropriate to send a card or write a letter if you cannot make a shiva call if you are out of town or for other reasons.