Read Mother Goose's nursery poems out loud so you can hear the rhymes (see link in Resources). Think about how entertaining they were to children in the past.
Sample some modern verses on Nursery Rhymes for Our Times (see Resources). Douglas Crockford's vocabulary isn't suitable for young children, but see how modern language breathes life into Mother Goose rhymes.
Buy a good rhyming dictionary or use Rhymezone (see Resources for the link). The rhymes in these poems have to be exact so a child can easily recite and remember them.
Think about building a child's vocabulary when you write your poems. Words like "movie," "phone" and "spaghetti" are suitable for young children and reflect what modern life is about.
Introduce children to the sound of the English language. Find words that are fun to say and have meaning for them. Choose "macaroni and cheese" over "curds and whey." Kids are more likely to have a pocket full of candy than posies.
Make the characters do things kids do or want to do. A rhyme like "Mary, Mary Quite Contrary" starts out well, but make your Mary annoy her parents and teachers. Make sure your characters get into plenty of trouble.
Read your rhymes into a tape recorder so you can play them back and catch awkward wording. Test your nursery rhymes on young children by doing a free reading at your local library. Mix your modern poems with Mother Goose rhymes and see how they respond.