1. First, please refer to the troubleshooting tips in the following article before you begin to map the network drive:
• Upgrade your IE to the latest version.
• Add your SharePoint Online sites to the trusted sites
http://support.microsoft.com/kb/2616712
2. Select the Keep me signed in check box when you sign in to your Office 365 accounthttp://portal.office.com .
3. After signing to Office 365, get to your OneDrive for Business, and copy the OneDrive for Business URL like https://contoso-my.sharepoint.com/personal/user_domain_com/documents/
4. Right-click the Computer icon from the desktop, and then click Map Network Drive.
5. Select a Drive and then paste the URL of the library you copied before in the Folder input box.
6. Make sure the check boxes of Reconnect at sign-in and Connect using different credentials are selected, and then click Finish.
7. Enter the username and password of your Office 365 when you are prompted to enter the credentials> Click OK.