I have been asked to give the prayer at rehearsal dinner, and I am not sure what to say. Can you please give me some guidance.

Goodness, what function will wedding planners dole out next? The servers have food ready to serve, and the people are hungry, no matter how religious they are, so just keep it short. Usually grace is about food and thankfulness and the gathering of people (ours ended with 'and make us ever mindful of the needs of others.') But this event isn't about bountiful harvest or charity, so I would say two sentences about blessing the two loving people and their wonderful families that are joining together.

I'm a preacher's kid and agree with Joy. Keep it short and thank God not only for the food but for the upcoming union of two families.

Here's a sample prayer you can adapt to your own religious beliefs:

Lord God, Creator of the universe, Father of us all, we have gathered here around this dinner table to celebrate the love and commitment that will unite [Name] and [Name] in a wonderful bond of marriage.

Bless, Father, this food that we are about to receive with grateful hearts as a sign of your continuous bounty and providence.

May your generous blessing descend also upon [Name] and [Name], their families, and their friends present here at this joyful banquet.

We make this prayer in the name of Jesus our Lord and Savior, who lives and reigns with You and the Holy Spirit, one God forever and ever. Amen.

So I take it, the pastor doing the wedding is not invited ( he would do it, and this would not be a issue)

But prayer can depend on what faith, Christian, Islam, Jewish, and even more divisions there. Will there be people at the dinner who may be offended by some wording ?

Simple and short