I think you may have meant your question for a specific school, as the answers to your questions (enrollment policies, procedures, deadlines; entrance exam, etc.) are best answered directly by the school your child will attend. You can locate the phone numbers for local schools (and school districts) in SchoolFinder: http://www.education.com/schoolfinder
The typical age for fourth grade is age 10. However, it really varies depending on the age the child started kindergarten, and whether or not the child skipped or repeated any grades.
Should your child be entering 4th grade this year, I'm including some information below to help get you acquainted to this grade in the U.S. I'm also including information about immunizations that are required by children entering U.S. schools.