I organized, analysed client needs. What is the best method for
presenting analysis information back to the client?
Based on the comments on the question, this information is going to be used to present a RFP to the client, as mentioned by Dhiman (+1!).
The key factor here as far as I can see, is to understand who is going to read this and how this analysis is going to be used. By the way, it seems you're already doing actual work, but the contract isn't firmed yet, which is a risk.
So, assuming the analysis is going to be used in a proposal, you could use any common format out there (like UML, mentioned by CG), but is vital to ensure that the client knows how to read it.
With that in mind, before using any format, I'd suggest to agree the format with the client before structure it. If the client understands UML, go for it. If client prefers good old PowerPoints, no problems. If prototypes are a possibility, even better. As long as you both know how the final product will look like.