Basically, a mesostic is just an acrostic in which the vertical word doesn't have to use only the first letter of each line, but can use any letter in the line. The lines are then indented in such a way as to line up the letters that spell the word. They're a lot more fun and easier to write than acrostics because you are not forced to start any line with any particular letter.
I've written quite a few mesostic poems for children. My general approach is to make the poem be a riddle and the word that is spelled down the center of the poem is the answer to the riddle. The poem can be presented with the letters filled in on the page, or with blanks that the child fills in as part of the strategy of solving the riddle.
I have my own mesostic variant in which the blank letters are not in order but require the child to unscramble them to spell the riddle's answer.