Hi S.,
I'm Jewish, and so here goes! In Judaism, one of the most important things you can do for others is to comfort the bereaved. Your presence will mean a lot to your friends, whether you know the customs or not. Nevertheless, here's the low down:
American Jews are varying degrees of religious. If you know the family is very religious (orthodox), then they would value modesty and you might want to wear sleeves (short is ok unless they are hasidic - just cover your shoulders) and avoid a low neckline out of respect. If the family is less religious, just wear whatever you would wear to any funeral. But honestly, in either case, just your being there will mean a lot to the family and override any thoughts about your dress.
Generally, there is a memorial service before the burial, followed by a short graveside service. Feel free to attend one or both. It is perfectly acceptable to attend the memorial service only, but whether you do both may depend on your relationship with the deceased. If you are close friends, your presence at graveside might help ease the pain of lowering a loved one into hard ground and leaving them behind.
If you opt to go to the graveside: at the very end of the service, attendees are invited to walk up to the grave, pick up a shovel, and spade some dirt into the grave. While this may seem a bit odd, it is considered an honor, a blessing and a last gift to help the departed to their final rest. Again, participation is a personal choice. The family will absolutely not be offended if you opt out. You will often see a husband, son or brother of the deceased wait until everyone walks away, and then finish filling the grave. It is a gesture very sweet and very sad at the same time.
After the burial, the family goes home, stays there for a few days, and receives visitors who come over to comfort them. This is called "sitting shiva," and depending on the family, it might last seven days (traditional - shiva translates as "seven") or three days. Usually there is visitation immediately after the burial service, but the officiating rabbi will make an announcement either way. There is also visitation every evening during the shiva (you need not go at all, but you are also free to go every night). While you are there, it is acceptable to circulate and talk to other visitors, and to eat and drink the food that is out. You should feel free to reminisce about the deceased, or to chat about anything at all within the bounds of propriety - your children, your job, whatever! It is also ok to simply sit near the family member(s) you know without talking much, as your simple presence will be comforting.
During this time, it is nice to bring or send food to the family, relieving the family of any worry about feeding all the visitors (or themselves). Sometimes friends will get together and organize to provide meals and to clean up around the kitchen, etc, during the shiva period. If you do bring food to the home of a religious family, you should stick to bringing a fresh fruit plate, or a veggie platter (without cheese or meat) on a new disposable platter, to make sure you don't breach the kosher laws (eating rules). Or you can call the Hen House at 119th & Nall and ask for the kosher butcher to put together some sort of a shiva tray for you. If you know the family doesn't keep kosher, you can bring over almost anything. Fruit and cheese. A salad. A deli tray. Your favorite casserole. A cake or cookies. Whatever. Even so, many Jews who don't keep kosher will avoid pork products, so you should avoid them too, just in case.
Each evening around 7 p.m. there will be a short "shiva service" led by a rabbi or a family member or friend. Sometimes right after the Shiva service, the leader will encourage people to offer a memory of the deceased aloud, but sometimes that doesn't happen. Anyone is welcome to attend the little service, but it's not mandatory. Visitors may drop by at their convenience during evening hours.
When you enter a shiva house, you may see certain other customs followed. There may be a pitcher of water and a basin just outside the front door, to wash/purify yourself before entering the shiva house. Once in, mirrors may be covered because vanity is inappropriate at this time. The family may wear their clothes torn in a spot, or pin on a piece of torn ribbon to signify their loss. The spouse, parents or children of the deceased may be sitting on a stool, bench or crate that is lower than the other furniture to show the depths of their sadness.
This is probably more than you ever wanted to know. But I think the real answer is - your presence will be greatly appreciated no matter what.