Here's the API call you're looking for. This will return you file IDs for every file in a specified folder:
http://developers.box.com/docs/#folders-retrieve-a-folders-items
You've got a few options for finding the folder ID. You can use the root folder, which has an ID of 0, so you can get the files and folders in there and continue inspecting your Box account based on those Ids. Or you can use the search API endpoint to search by keyword and return folder and file IDs.
http://developers.box.com/docs/#search-searching-a-users-account