Method 1: Download and install Outlook.com app from the play store. Sign-in using the Microsoft account to which you have backup your contacts and now open the app Go to Settings > Contacts and Calender and enable the contact sync & calender.
Now your phone will automatically sync the contacts and calender from your Microsoft account whenever you are connected to internet.
Method 2: Now the another method is open Outlook.com from your browser. Sign-in using your Microsoft account.
Go to People, now select Manage >Export and save the file to your Phone memory or SD card.
Now on your phone open Contacts and go to Options > Import/Export > Select the location where you have saved the file.
However you cannot restore the Calender through this method.