How can I start a pet sitting home-based business?

If you have a dog yourself you could go to a dog park and make some connections there. And if you don't have a dog, good luck.
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I have in the past. However, I prefer the pet-sitter to come to my home and feed my dog, take her for a walk, etc.. You really need to network. Talk to the people you know that have pets, offer the service. Talk to your vet -- they probably get a lot of requests. Once you've been able to do this service for a few people, let them know you're always looking for new customers. If they are satisfied with your performance, they will recommend you to friends.
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you can always put up news paper ads, leave cards at vet clinics etc. gl
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Hi - My sister has created a very successful pet sitting business. She started out letting friends know she was available. By word of mouth, she has become very popular. A few ideas of where to get customers - there is always the bulletin board at the grocery store, pet store or vets. You can also have business cards made (I highly recommend this - for a professional appearance and ease of getting the information out to prospective clients - and they are cheap to make now days) She also spoke with local realtors, since they sell homes and such, and give advise on shopping, beauty shops, other local businesses to prospective buyers. There is always the newspaper too, or door-to-door. It helps to have a little resume made up for perspective clients (what kinds of pets you are willing to care for, what experience you have had) and you need to think about rates too. Good luck. To answer your question about being gone and what would I do - we leave our pets at home and a family member tends them. My sister goes to the people's homes - she doesn't bring the animals to her house. As a side line, you can also bring in mail, newspaper, water plants, etc for out-of-towners. You might want to look into getting bonded if you are going into it that far.
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I live in a gated community has has a local magazine that comes out once a month that people advertise in. We have several sitters to call on when in need of a pet sitter. Also I volunteer for our local no kill animal shelter and they have a list of people that cover different areas of the city and people call them for referred sitters. They go to the home twice a day and feed, water and walk or let the animals outside for exercise and play with them. Check with your shelter. Good Luck!
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Friends for Animals Volunteer, Granbury, TX