You should be able to go into the contact list and save a version of it as a file.
1. Go into your contacts list and click the "Menu" icon (three dots).
2. In the list of options there you should see an "Import/Export" one listed. Tap that.
3. Next choose the "Export to storage".
4. You should now get a little pop up window saying the location it will be saved to, and the file name.
5. Click "OK" to have it create the file.
6. Now you can connect the phone to your computer and copy or move that file over to the computer.