I have found three ways to upload courses to the Edge 810. It would be nice if I didn't have to convert GPX file types but otherwise it works fine. On the last scenario, I can do 100% of this from my Android phone.
1. Manual Upload to Garmin Connect, then transfer to Edge with Garmin Express.
Save the file as a GPX tracks file or convert it to GPX tracks with GPSies
Go to Garmin Connect
Go to Activities, then click on Import upper right corner.
Click on Choose File then locate a tcx or gpx file (or fit file)
Click on Upload Activities from file
Click on the activity then click on settings in upper right corner
Save as Course
Go to Courses and click on the Course you want to transfer
Click on Send to Device upper right corner
Send to Device
Garmin Express will open and sync the file to the Edge 810, it may ask you to install updates, so click on update.
2. Transfer file to Garmin folder connected to the computer as a drive.
Save a gpx file on the computer,
Plug in the Edge 810 to the USB port
If the computer doesn't recognize the Edge 810 click on Garmin Express and wait for it to find the Edge 810
Open Windows Explorer and find the Transfer the file into the Garmin folder on the Edge 810 folder
Open the Garmin Folder and find the NewFiles folder.
Transfer the Gpx file into the NewFiles Folder
Click on the application tray and safely remove hardware/eject device.
It will show up on the Edge 810 as a course.
3. Upload to Edge 810 using Garmin Connect Mobile
Save the file as a GPX tracks file or convert it to GPX tracks on www.GPSies
Go to Garmin Connect
Go to Activities, then click on Import upper right corner.
Click on Choose File then locate a tcx or gpx file (or fit file)
Click on Upload Activities from file
Click on the activity then click on settings in upper right corner
Save as Course
Go to Garmin Connect App and refresh, then click on courses, then refresh, then click on course, then click on the arrow on the upper right and the Edge 810 will indicate Downloading Course/Download Complete and the Phone will indicate it is syncing with Edge 810
If you can't upload the files in Garmin Connect because of an error when uploading use the GPSies site to convert the file.