If you are attaching files via Dropbox, you will be asked to log in to your Dropbox account, and then your Dropbox files will appear in your chooser. You can attach existing files, search through your Dropbox files, or add a new file from your computer. The new files will be added to your Dropbox and attached to the task simultaneously. This way, you can share files even if they are not already in your Dropbox.
The files can be accessed by you and anyone you share the project with from the expanded view. Your team members will be able to open the files, download them and save them to their own Dropbox account.
If you are attaching files via Google Drive, you will get a Google Drive file selector, where you can select the files you want to add to your tasks. The selected files are then attached to the task, and can be accessed by your team members. The files open in Google Drive, so you will be all collaborating on the same document.
A file attachment label appears next to tasks with attached files. This way you will be able to tell if there are files attached without opening the task expanded view.