To use iTunes to copy files to any app other than one of the built in media apps (Music, iBooks, TV, etc). (Most, but not all apps support iTunes File Sharing).
- Plug the iPad into the computer.
- Open iTunes and select the iPad in the tool bar.
- Choose the Apps Library from the left screen.
- Scroll the donw right screen until you see the File Sharing tools.
- Select your app from the list.
- Drag or Copy/Paste documents to/rom the Documents window.
It is not necessary to Sync the Pad when using this tool. The files are transfered immediately.
If you have a Mac and use iCloud Drive, you can bypass this by using the iCloud Drive folder and app on the Mac and iPad (respectivly).
In windows you could use the iCloud.com site to copy files to/from the computer. They will sync to the iPad automatically.
Both of these require the app to suppoert iCloud Drive. I'm not sure if Adobe Reader does, but many other good PDF apps do.
You can also use Dropbox or other cloud service and apps to easily move files between the computer and iPad.
And some apps support the ability to transfer files via your computer's web browser, as long as they are on the same wi-fi network. Look for a Wi-Fi option. It will supply an IP addres that you can enter in the computer's browser.
Personally, I tend to use iCloud Drive, DropBox, or the other wireless methods. Unless I've got a ton of big files to move, iTunes File Sharing is more trouble than it's worth.