Microsoft maintains the instructions for different Outlook.com versions here.
For the latest version (when we last checked), the steps were:
- Go to Outlook.com (if not signed in, click Sign In.)
- Once signed in, click on the People icon near the bottom left.
- From the top menu click Manage.
- From the options that show up, click Export contacts.
- Choose to export all contacts. You may also select a specific folder if desired.
- Click Save and contacts.csv will be saved by your browser, typically to your Downloads folder.
Once you have your contacts saved to a file above, import contacts from that file as explained here.