You can run a variety of reports on foster people and animals depending on what information you are looking for. Take a look at this article here for details on pre-made reports: What quick reports are available in Shelterluv? and this article here on building custom reports: How do I run custom reports?
I would suggest exploring the Foster Quick Reports here:
And to report solely on people records marked with the willing foster attribute, you can run a Custom Entities Persons Report with a rule for Attributes matching Willing Foster (assuming your people records have this attribute marked):