You will enter the donation as a charitable contribution. When entering this information, you will need to know the name of the charity or organization who placed the exchange student with you. The donation will be entered as a 'cash' donation using the guidelines in the IRS publication you shared to determine the amount.
The following TurboTax help article will give you explicit instructions about where to enter this donation amount in your return:
How do I enter my 2024 charitable donations in TurboTax?