Does the app offer an email sharing option? Most do. Open the document and look for a box icon with an arrow coming out of it. That's where it usually hides.
You may find an Open In option as well. If you do then you could use this to copy the file to most cloud service apps (DropBox, Box, Google Drive), where you'll get the option to upload it. Installing the same service on your computer would automatically copy the file to the associated folder there.
Those are the standard, most common, and usually easiest methods. The may be others. Find your app in the App Store, read the descriptions, and/or follow the link to the developer's website to see if they mention any others.