If you have an Office 365 mailbox, you can access it over the Internet, just like you sign in to Facebook, Gmail, or Amazon. It looks like this: 

What the ribbon looks like when you have Outlook on the web.

To import your contacts to your Office 365 mailbox, you need to use Outlook 2016, 2013, 2010, or 2007. When you launch Outlook, you'll see "File" in the top left corner: 

What the ribbon looks like in Outlook 2016

To import contacts to your Office 365 email account:

  1. Export your contacts from your "source" email service: 

  2. Add your Office 365 email account to Outlook. 

    Outlook will sync with your Office 365 mailbox. After a while, you'll see a copy of your email and contacts in Outlook. 

  3. Use the import instructions on this page for Outlook 2016, 2013, or 2010 to import a CSV file or .pst file that has your contacts. 

If you don't have Outlook installed on your computer, see How to get Outlook for your desktop.