Map a SharePoint document library to your desktop

Mapped Network Drive

Application Layer (Internet Explorer):

Internet Explorer > Internet Options > Security > Trusted Sites (tab) > add the SharePoint Online Site collection to it (include https://)
Internet Explorer > Internet Options > Security > Trusted Sites (tab) > add https://*.sharepoint.com
Internet Explorer > Internet Options > Security > Trusted Sites (tab) > Custom Level > automatic logon with current username and password
Require server verification (https:) for all sites in this zone should be checked

Internet Explorer > Internet Options > Security > Local Intranet (tab) > Advanced > add the SharePoint Online site without https:// Internet Explorer > Internet Options > Security > Trusted Sites (tab) > add *.sharepoint.com
Internet Explorer > Internet Options > Security > Local Intranet (tab > Custom Level > automatic logon with current username and password
Require server verification (https:) for all sites in this zone should be NOT be checked

Presentation Layer (Operating System (Windows)):

On the computer – Start > RUN > services.msc > WebClient > Set it to automatic

https://support.microsoft.com/en-us/kb/2629108
We then go to the document library > Open with Explorer > copy the URL – Copy the URL and mapped a network drive on the computer.
Open explorer on the Computer
Right click Computer > Map a network Drive
Enter the URL for the document library > Finish
http://support.microsoft.com/en-gb/kb/2616712
http://support.microsoft.com/en-gb/kb/174360

Every 8 hours an access token would need to refreshed or else we might see a red X on the network drives.