No matter what kind of solution is deemed the fastest, the best, or the cheapest, it is all going to cost some monetary value. This issue is affect a large portion of India, both in population and geographically. I think it is just as important to consider how and who will pay for this expenditure as it is to think of how the water and sanitation will be implemented.
The least expensive way to get sanitation, as far as sewage, would be composting toilets. That would essentially just be having a hole in the ground to go "number 2" and to aid it along to becoming good fertilized dirt again. So naturally education will also need to be a part of this as well.
For water, the infrastructure of trying to move a massive amount across a wide spread of the country is going to take a very large infrastructure. Wells are another option that has been stated, as well as filtration, desalinization, and so on. For all of these options to be effective and reach the large amount of people that needs to, it is going to take a lot of money.
In total money is going to be a major part of what will get this done. But where will it all come from? Charity? Volunteers providing labor? Well it be up to Indian citizens or will the whole world get involved. Hopefully every option will be exploited and that will help this get done. Leverage businesses to bring volunteers and donate a small percentage of their profits at the end of their year. (thinking along the lines of Salesforce's 1/1/1 plan).