Brainstorm to come up with a list of all the things you know about the subject of you dedication poem. Think creatively. Sometimes a small gesture or thing that you remember may not seem significant but can add color or nuance to the dedication. Don't leave out charming or humorous details, which can provide levity in the right circumstances.
Select a rhythmic format for your poem. Iambic pentameter is a good format, as it is quite rhythmic and recognizable. It consists of five, two-beat measures per line, with the accent on the second beat (dee-DUM, dee-DUM, dee-DUM, dee-DUM, dee-DUM). A famous example from Shakespeare is his sonnet that begins, "Shall I compare thee to a summer's day?"
Decide whether you want the dedication poem to rhyme. Rhyming can be more musical, but it will limit your word choices. You don't have to rhyme the poem; write it in blank verse, a poem in iambic pentameter that doesn't rhyme.
Begin to structure your lines from your brainstorming list. You don't have to write the poem sequentially, just start by getting the things you want to talk about into the rhythmic format (meter) you have chosen for the poem.
Arrange your material once your lines are composed, editing and restyling as necessary for your rhyme scheme. Be considerate of your listeners with regard to length. Less is more, and a poem that lasts from one to two minutes (20-40 lines) has plenty of room for material without going on too long.