Visiting a funeral or wake requires respect and decorum.

Greeting and Arrival:
You should arrive on time, preferably a little earlier to pay respect to the family and the ceremony. Quietly enter and, if the service has already begun, wait for an appropriate moment to take a seat in the back. Words can go a long way in greeting the family; keep it simple and sincere: "I'm so sorry to see you're going through this" or "You're in my thoughts." Do not tarry long at the wake; a heartfelt brief visit is often enough.

Wearing
Be dressed modestly for respect. Traditional attire may be black or dark coloration. A suit and tie is standard for men, a collared shirt and slacks acceptable, while for women, they should dress modestly; a dress, blouse and skirt, or slacks are common, but should not include bright colors or flashy jewelry.

If the family desires you to dress in some specific attire, such as wearing a particular color, to honor the deceased, you should try to comply with their request.

During the Service:
Cell phone turned off and unnecessary movement; sit unless requested to get involved in the service; listen actively and only react when a hymn should be sung or prayed as part of the service; bow or gestures of respect are seen as the order of things in some places, do as others when you do not know;
Be brief, and be positive so you honor the person gone.

Speaking to the bereaved is a time to keep things simple. Sometimes, that's enough. Telling them you are there is much more important than making a speech on what to do or how to act. Do not use your time to share your losses with them. This moment should be about the loved one and their family.

After the Service: 
If you are asked to stay for the service, then join in on a reception or dinner that goes on in honor of the deceased loved one. Provide support, but don't impose yourself when there is family time.

In short, there is very real concern for those grieving within a respectful attendance, proper dress, and proper, sincere words of sympathy. Keep actions simple but meaningful for the significance of the event.

ALSO READ:

Funerary Dressing Guide