If you are new to house sitting this is what you should be doing.
House sitting references. The quickest way to get house sitting references that can be verified is to apply for any small jobs (2 to 7 days) in or near your current location or in not so desirable locations that you can do at any time. (You can look for longer sits in your preferred locations later). There is much less, if any, competition for very short term positions (hence easier to get especially if the home owner knows you live nearby). You will find 2 to 7 day house sits are easy to do as the home barely has time to need cleaning or the garden have time to become overgrown. Also, if you can leave the house cleaner and tidier than you found it, you are sure to get a glowing reference.
Get a Police clearance if you don't already have one. It's a document from your state government stating whether or not you have a police record. They cost up to $50 and take 3 weeks or so to arrive. Search on line for "Police clearance" followed by your state (use the website with .gov in the web address). You can also call in at your local police station and pick up an application form.
When you have 2 references (but don't stop at 2) and your police clearance, keep copies of them on your computer and attach them to all 'first contact' messages you send to home owners. If you can provide those items without having to be asked, the home owners won't spend time with other applicants that haven't provided them yet. In fact many experienced sitters don't use scanned references although they do have them, they ask the home owners they have house sat for if it's ok if other home owners ring them for a verbal reference - they then include their names and phone numbers in their first contact message to home owners.
Be one of the first. Many home owners only look closely at the first few sitters that contact them and pay less attention to the others that follow. And if they 'click' with someone early on in their search, any others that come later and may be better suited get overlooked. So you should try to be one of the first to contact an owner. Experienced sitters won't wait for the daily notification of new positions, they check the website sometimes twice a day to make sure that, if there is a job posted that suites them, they are one of the first to contact the home owner.
Your profile and your introductory message to the home owners are very important in creating a great first impression. Your profile, which should include a photo of yourself, should be mostly about what you can do for the home owner, not about you or your family. It should make the home owner think "This person is perfectly suited for my needs". Initially home owners will only be interested in hearing about what you can do for them, not about your reasons for wanting a particular house sitting position; you can tell them more about yourself later. If you are or were a home or pet owner you should tell them as it indicates you are familiar with what's required in looking after and maintaining a property and pets.
Your opening message to them should not be short, such as "Hi I am available for your dates". It should be a brief description of what you can do for them and their pets. Name their pets in your message and if they have photos of their pets in their ads, comment on them.
Include your phone number in your first contact message as many people prefer to use the phone instead of the internet. It's easier for them to pick up the phone and call you then it is for them to write an email and wait for a response.