Dressing for a wake is all about respect; respect for the deceased, and respect for the family. This means dressing in a toned-down manner.
You don't have to wear black to a wake, unless you are immediate family. Many people erroneously believe that one must wear black to a wake, no matter the relation to the deceased. But any dark tone is fine, and it doesn't have to be dark for all pieces. You can wear navy or brown or even grey to a wake. If a woman, either wear a pantsuit or skirt with blouse. You can pair these with a white blouse if you like, but stay away from bright colors like red, pink, yellow or orange. White is simple, and is a perfect accompaniment to a dark suit or dark skirt.
If a man, a dark suit, or dark pants with jacket, are perfect. Again, men can pair with a white shirt, if they like, and a tie is always the perfect accessory for a wake. Think in terms of attending a very important meeting with someone you want to impress, but not stand out inappropriately, and that's how to dress for a wake. You want to look nice, but not too sharp or with too much personality. Somber is the theme, here.
No jeans. Don't even think of wearing jeans, or even sneakers. Even if the deceased was a beach bum, you want to show respect and not look as though you, yourself, could be going to the beach or a beach bar.
Women, avoid open-toed shoes. Even if this is the fashion, open-toed shoes are inappropriate at a wake. You want to look as though you're going to an important dinner, not to a club. Also, if wearing pants, be sure they are well-pressed. Cleavage should be covered, as should legs. Keep the word "respect" in mind when dressing, and you'll make the right clothing choices.