By answering these 12 questions, you'll find problems in any (seemingly) tight process. Now you've removed non-essential steps, it's time to automate as much as the remainder as possible.
If you're using paper, there's almost certainly an electronic solution that can eliminate that, whether it's signing documents or just managing them.
If you're transferring data between your apps (adding Dropbox files manually to Google Drive, for example), you'll certainly find a solution with Zapier, which lets you set up a rule for all future actions that meet a specific criteria. For example, 'whenever a new file is added to Dropbox, transfer it to Drive'.
Think in the most efficient terms for the whole process by reading our ultimate guide to business process automation.