I don't know how you would go about applying for the projects in USA, but it is likely to be similar to UK where you apply to a university stating which area you would like to research. The duration of a PhD in the USA is 5 years (I think!), it is 3 years in UK. The fees would be expensive. However it may be possible to be funded. For computer science, perhaps MIT would be a good choice, this is one of the best universities in the world, so it would be competitive to get a place there