CUDA is (mainly marketed as) an extension of the C language… If you do not know C, you might want to google a few tutorials to teach yourself how to do basic things like variable manipulation, file input/output, etc. It might be that some CUDA tutorial also emcompasses the basics of C language as well, but I’m not aware of any.
As far as suggestions… set up the CUDA SDK on your PC… and look at the examples given, manipulate them, run other examples, compile your own programs… that’s a good way to learn.
If whatever algorithm you have (or plan to do) benefits from parallelization techniques to speed it up, then CUDA would be a good way to exploit that. For that matter you don’t need to use CUDA, you can also learn OpenCL, which is compatible with both AMD and NVIDIA cards – the basis is the same, it’s an extension of C language to run programs on GPUs and take advantage of the inherent parallelism.