Men remove their right glove to shake hands on the street, but leave them on when shaking hands at the opera or a ball. If it is too awkward to remove the glove to shake hands, the man must apologize for not removing his glove. Women do not remove their gloves to shake hands, except with the head of a church or a head of state.
Gentlemen only wear white gloves at the opera, a ball, or as an usher in a wedding. Part of the reason men wear gloves at a ball is to avoid putting their sweaty hands on a woman’s bare back (cause, gross) or damaging their gown with the sweatiness. Men can wear gray doeskin gloves on the street. Amy Vanderbilt advises that while going gloveless in winter may make a man feel hardier, it results in chapped hands (again, gross.)
Ladies wear gloves to formal dinners and take them off at the table- the gloves go on your lap and the napkin over the gloves. Women’s formal gloves are white kidskin (this means a very fine, thin, soft leather) and are the most luxurious thing because they must be thrown out as soon as they get dirty (which probably takes about 5 minutes.)
Women remove gloves during church to make it easier to handle the prayer books, and definitely removed them for communion. As with shaking hands, women keep gloves on during a receiving line (except, again, with heads of state and the like).
Stylewise, bracelets can be worn over gloves but rings cannot be. One very old etiquette book mentions that you should be fully dressed before leaving your house and pulling your gloves on in the street is the height of ill-breeding.
Brides who wear gloves either take the left one off before the ring is put on or they split the seam of the ring finger so the ring can slide on.
Sources: Etiquette by Emily Post and Amy Vanderbilt’s New Complete Book of Etiquette by Amy Vanderbilt