Tips for an Effective Child Permission Letter List important information about your child and any other relevant info. Mention the scope of what you are/aren't permitting. Note what time period the authorization applies for. Include your contact info and sign your name with a witness present.
In the USA, though, unless there's a court order requiring permission from both parents, a child may travel (even to overseas) with either parent/guardian without showing proof of permission from the other parent.
You need to obtain a passport for your child if he/she will be traveling overseas. Your country has requirements for getting a birth certificate for your child, and your government's passport office will tell you what other documents may be used as alternatives.
A parent generally needs permission from the other parent before travelling with the child especially if the travel will impact the parenting time of the other parent. However, if the separation agreement dictates how travel should occur, both parents are expected to follow the terms of the agreement.