How will I know if my child is developing normally?

Pediatrician visits. The first two years seeing the pediatrician focus on development. At each visit we go over development and what your baby is doing now and what should be achieving by the next visit. Discuss with your doctor what books are worth reading on this subject.
Checkups. Sometimes, esp. As a new parent, one might not know what is normal or what is not. That is the job of your pediatrician to determine that. Which is why well checkups are very important because developmental questions should be asked by doctor at that visit or any concerns from parents should be made aware.