Remote consulting exists, but it's harder to find work that way -- infinitely so if you have no reputation.
The only advice I can really offer on how to get started is to network. Talk to people about their problems at work and take genuine interest, even when they're not a potential client. Where possible, help people out in meaningful ways and show (don't tell) them that you're smart and that their problems are important to you. You'll probably end up doing some free work this way, but you'll make friends who trust you and that's far, far more valuable. As long as you're clear that you're looking for consulting work, it'll find you eventually. Just don't belabor the point.
One trick of mine is to focus on selling the minimum amount of complexity. Figure out exactly the value that the customer is looking for - often times they don't know what it is. There's a saying that a person in a hardware store looking for a quarter inch drill doesn't need a quarter inch drill, they need a quarter inch hole. But more importantly almost nobody needs a quarter inch hole -- maybe they need a new shelf. If they need a new shelf, maybe they just have too much stuff. No matter what it is, get to the bottom of their problem and sell them the simplest solution with the maximum value, even if it doesn't make you any money today.
Also consider trying to tackle some stickier problems in well-known open source projects. PostgreSQL is a favorite example of mine for this as they make it very easy to contribute. Why hire someone who "knows" PostgreSQL when you can hire someone who helps write PostgreSQL?