Check the diaper frequently, and change it when wet.
Use a gentle perfume-free soap or even just plain water when cleaning the area. Make sure the diaper area is clean and dry before putting on a fresh diaper.
If you use wipes during diaper change, avoid wipes with fragrance or alcohol. Use ones that are mild and designed for baby's skin. Gently pat the area clean and avoid rubbing the area clean.
Let your baby's bottom "hang in the breeze." There is nothing better to dry out the area than taking the diaper off for a while whenever the coast is clear (e.g., right after cleaning off a bowel movement).
Consider changing the brand or type of diaper. Cloth diapers tend to cause fewer rashes because they don't hold in the liquid as well. And some parents have better luck with one brand of disposable diaper over another.
Keep the diapers a bit loose so some air can come in and the area can "breathe." *Avoid plastic pants, which hold the moisture in.
When washing cloth diapers, put a half cup of vinegar in the rinse cycle to help get rid of alkaline irritants.
Use a protective barrier cream or ointment on the area after each diaper change. In general, those with zinc oxide give the best protection from irritation (but are a bit stickier). But often the less sticky petroleum products work just fine.
Consider an over-the-counter steroid cream to decrease redness and inflammation (but consult your pediatrician before using them).
If you use baby powder, pour it out carefully and keep the powder away from the baby's face. Talc or cornstarch in baby powder can injure a baby's lungs.