If you have EAGLE files on your Dropbox you can import them directly from Copper. You will need to connect Copper to your Dropbox. Copper is then able to read content from your Dropbox. If you don't want to do that, you can also use the Dropbox App or Website to download a file (EAGLE or Zip file) and send it to Copper. This is described in this article: Sending content from other iOS apps.
Giving Copper access to your Dropbox
Before Copper can have access to your Dropbox you must give the rights to do so. You will be redirected to the Dropbox App on your iPhone or to the Dropbox webpage in Safari.
Please follow the instructions to give Copper access to your Dropbox.
Navigate your browsers and choose a file
Once you have given access you can add files from Dropbox to your Copper library. Tap the + button in the library as described above (again) and choose Dropbox from the source list.
You will now presented a screen that looks similar to this one:
Once you have selected the file Copper will start downloading the files. Copper will always try to download the layout (.brd), schematics (.sch) and Copper settings file (.cop). So it does not matter which file you choose.
Copper will show you the library and will start downloading and processing the files. Once the thumbnail is shown you can tap on it to open the file. The project will stay in your library until you delete it.
Downloading a ZIP file
If you download a ZIP file, Copper will download that file and examine its content. You will then be presented with a screen that let's you choose which files Copper found in the ZIP should be imported.
Once you have made your selection you are brought back to the library screen where the new files should be presented. It might take a few seconds until the thumbnail image is rendered.