"The Cloud" is just a bunch of machines that you don't own. Running on those machines is no different than running on the machines that you do own, except that you pay for the time and bandwidth.
If you're using a tool like Hadoop, adding machines is just a matter of configuration (you don't mention platform, but it's the main player in the non-Google map-reduce space, which is just one of the big-data techniques).
My recommendation is that you work through the tutorial, get a single-node implementation of your application running, then immediately move to a cloud service like Amazon EC2. You can start with two small instances for about a dollar a day, and increase the number of machines from there.
As a cautionary note: unless you're dealing with 100s of gigabytes of data (and preferably terabytes), I don't think you'll see much benefit of either horizontal scaling or "the cloud." There is a not-insignificant time to setup and teardown map-reduce operations.