To see what this looks like on the parent side check out this article.
1. Search for the app you would like to download in the iTunes App Store and tap Get and then Install.
2. Type in your Apple ID password and tap OK.
3. If your parent has on the Ask to Buy feature you will be prompted with a pop-up to Ask Permission. Tap Ask.
4. Notice the app will grey out letting you know that you have requested the app.
5. Once the owner of the Family Share has Approved the request, you will receive a notification. If your request was approved then the app will begin to download. If it was declined then it will not download.