Office 365: Share a Document

1.  If you've just created the file, and it's open, click the 'Share' button in the upper-right.

If the document was created previously, you can click the 'Share' button on it's entry in your Document library.

2.  This brings up a dialog box.  Click on the address line, and begin typing an email address or name.  Press enter, or click on the entry for the person you want.  Continue adding people as desired.

3.  When you have all of your intended recipients selected, add a brief message in the message box, and click 'Send'.

Each selected user will get an email with a link to the document.