Usually at Jewish funerals, they are not to mourn, but to be joyful. I am sure though that you will see people mourning with pain

Wear black, as you may have guessed. Long sleeves and long skirt preferably, but it depends on how observant the ceremony will be. If it is Reform you can get away with short sleeves but stay away from sleeveless. It is a good idea to not wear anything that shows your legs at all. Any religious event both girls and boys are asked to cover their heads. You will not need to supply your own head covering. If they expect you to cover your head they will have little lace for the girls and a yamicha, or keepah, for the boys.

If the family is really traditional they may separate the men and women so be observant and try to notice what everyone else is doing. You may find this to be an interesting learning experience. The Jewish religion is filled with ancient traditions.

For a woman, you should be modest dressed. Wear a long skirt to the ankles and a blouse that is not low-cut. Just dress decent. Most of the Jewish women who are religious do wear a head covering or a scarf if you are married. Do not dress like you are going to some party or night club, use common sense of being respectful.