On Friday night (or the night of Yom Tov), we generally begin the meal by reciting Kiddush, after which we wash our hands and then recite the Beracha over bread. In some situations, however, people might prefer washing their hands before the recitation of Kiddush. On Sukkot, for example, it may be difficult to bring everybody back from the Sukka into the house after Kiddush for Netilat Yadayim, and some families therefore prefer having everybody first wash their hands before entering the the Sukka for Kiddush. This is common also at affairs held on Shabbat, where people might not want to leave their seats for Netilat Yadayim after Kiddush. What is the proper procedure to follow in such a case?
The Shulchan Aruch writes explicitly (271:12; listen to audio for precise citation) that if one washes his hands before reciting Kiddush, then he must recite Kiddush over bread. By washing one's hands before Kiddush, he demonstrates that he considers the bread primary to the wine, and he must therefore recite the Beracha over the bread before reciting the Beracha over the wine. He therefore recites Kiddush over the bread, and may not first recite Kiddush over wine.
One may, however, listen to the recitation of Kiddush over wine, and answer "Amen," after washing his hands. Therefore, if everybody at a meal washed their hands before Kiddush, with the exception of one person who did not, he should recite Kiddush over wine on behalf of the others, who should answer "Amen" and then recite the Beracha over the bread. (Menuhat Ahava, Helek 1, page 143.)
Summary: Generally speaking, one recites Kiddush on Friday night (or the night of Yom Tov) before washing his hands for bread. If somebody washed his hands before reciting Kiddush, he should either listen to the recitation of Kiddush over wine by somebody who had not washed his hands, or recite Kiddush over bread.