Adding files is pretty straightforward. Head over to your Boards and you'll find a menu bar with all the different types of items you can add to your Boards. Forth tab along you'll find Files. Click on this and it'll bring up your list of available Files plus the Add File button highlighted in blue at the top right.
Add File will bring up your handy File Upload manager. Simply drag and drop onto the upload section or use the Browse function to choose the File from your computer.
You'll need to have a paid plan in order to support File sharing. The More Mesh plan includes 2GB of file storage whilst the top tier Most Mesh plan includes 10GB of file storage.