If you think you might want to foster, go to the website of the rescue group you want to work with and there should be an application there. The reputable rescues (like Yorkie Haven Rescue, YTNR, etc.) will do a very thorough check ....veterinary history, home visit, etc., before approving your application.
I just started fostering for YHR a few months ago and I am loving it. But, I don't have much experience yet so I don't want to advise you incorrectly about making introductions. There are very experienced rescue workers on YT who'll be a great help to you, and your rescue group should also assign you a mentor who will be glad to help you with any questions, concerns, etc.
Good luck!!!
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