Read the whole poem. Reread the first line. Try to recite just the first line without looking - let the students check you. Explain that they are to go through the whole poem in that manner. Older students, ages 10 and up can perform the poem as a rap.
Students can also try to write their own poem that teaches the order of the planets.
Have students recite the poem individually, in pairs, or in small groups. Memorizing a poem is one way to get it there.