Install Design on WordPress

I am re-doing a website for a non-profit organization. We installed WordPress on it, its being hosted at GoDaddy. I bought the Thesis theme for it, and hired a contractor through Elance to help design a customized WordPress design for my website.

He says that he can either have access to my hosting account to install the files, or transfer the files to me and I can install them myself. I actually do not have access to the hosting account, only to the FTP.

Out of safety, I would prefer to install the files myself. I know I can do this, I just do not know how. Can somebody please explain this to me? Thank you!