Click on Files in the bottom navigation bar of the project.
You may browse your computer by pressing the "Upload a file" button by the page title, or you may drag and drop files into the area to upload them.
Alternatively, you can upload files directly into a discussion or task and they will be shown in the Files tab of the project.
Note: Nifty currently allows the upload of .sketch, .psd, .ai, .doc, .docx, .pdf, .csv, .xls, .jpeg, .png, .gif, .avi, .mov, .mp3, .mp4, .aac files.