When I was a missionary, I heard this question a few times.

The Bible verses in question are these (Matt 22:23-30)

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The same day came to him the Sadducees, which say that there is no resurrection, and asked him,

Saying, Master, Moses said, If a man die, having no children, his brother shall marry his wife, and raise up seed unto his brother.

Now there were with us seven brethren: and the first, when he had married a wife, deceased, and, having no issue, left his wife unto his brother:

Likewise the second also, and the third, unto the seventh.

And last of all the woman died also.

Therefore in the resurrection whose wife shall she be of the seven? for they all had her.

Jesus answered and said unto them, Ye do err, not knowing the scriptures, nor the power of God.

For in the resurrection they neither marry, nor are given in marriage, but are as the angels of God in heaven.

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The way I fit those verses into Mormon doctrine is to interpret them to mean that the initiation of a marriage (to "marry," or to "give in marriage") belongs to mortality-- one may only be married in this life (or by proxy, as per the usual LDS temple doctrine). Thus, the word "marriage" in those verses refers to the ceremony rather than the relationship. The English word "marriage" has at least those two meanings; I don't know if the Hebrew bears out my interpretation.

Of course, if it does not, I will rely on the standard Mormon "tactic" of claiming an error in the recording and/or transmission of Christ's words... ;-)