So by mentioning salary I presume we're talking indefinite contracts here rather than lots of different clients.
To be honest you're going to have a tough time, competition is high and hiring juniors seems quite rare. (You may have more luck with larger remote companies but most remote companies tend towards the smaller side).
However here are some things you can do to maximise your chances (applicable to non remote work too).
1. Be effective and clear with communication, remote work requires you to over-communicate. Don't assume the person with whom you're talking to via email/slack has all the information that you do.
2. Being a grad you've got no real CV experience to fall back on, imperative that you have a github/bitbucket account with examples of the work you can do. At least one fully fledged project in the stack that you are targeting. For example if you're going to work with Rails then having a project where you use some common libraries, integrate OAuth or some sort of authentication,talk to external APIs with good test coverage and and documentation.
3. Almost as important as #2 is to blog with what you're learning, show any companies of the learning that you're doing and the potential that you have. We had an applicant once who included a link to all 50 Amazon reviews he'd written of different tech books, fantastic way to show passion and understanding.
4. Be realistic, being a grad and go straight into remote work will be tough. Have a plan B.
My advice would be to try and work in a larger company for a while, find the opportunity to work with experienced developers and see how it is, you may actually like being in an office! Remote work is not for everyone and while it seems to be perfect it has many drawbacks.
Best of luck!