The gift for the groom can be tradional or nontraditional. So it is a simple handkerchief, a thoughtful letter, or elegant cuff links. A ticket for a concert or sports event. A funny card may do. A great t shirt are some options.
When to give the gift? It depends tradition and culture. If these things do not pertain to you, at the rehearsal dinner,before the wedding, or on your honeymoon.