Age Range Covered:
IDEA 2004 specifies that FAPE must be made available to all children residing in the state between the ages of 3 and 21 inclusive.
34 C.F.R. 300.101(a).
Eligibility At Age 3:
School Districts are required to make FAPE available to children with disabilities by no later than the child's third birthday. 34 C.F.R. 300.101(b). The law specifies that the IEP must be "in effect for the child by that date," meaning that assessments to determine eligibility and an IEP meeting to develop goals, services, placement, etc, should be held prior to the third birthday.
If the child turns three during the summer months, IDEA allows for the IEP team to determine the date upon which the IEP will begin. 34 C.F.R. 300.101(b). However, this should be read in conjunction with the requirement that an IEP be in place at the start of the school year for each child with a disability residing within the district. 34 C.F.R. 300.323(a).
Eligibility To Age 21:
States are permitted to decide how to determine the end date for eligibility for a 21 year old. Some states may cut off eligibility as of the date that a child turns 21. Others may determine that eligibility goes until the end of the semester or school year in which the child turns 21. Still others may determine that the child would remain eligible throughout their 21st year (i.e. until they turn 22).
Keep in mind that being age-eligible is not the same thing as an automatic determination that the child still requires special education and related services. There are other factors used to determine the end of a child's special education program for students beyond "school age," such as graduation from high school with a diploma or certificate of completion, an IEP team determination that the goals have been met and services are no longer required, etc.