If you do not have an Office Desktop license, you are probably using Outlook Online. Otherwise, you should use Outlook Desktop.

In the top right, click the Settings cog, then "View all Outlook settings":

Then, click on "Compose and Reply" and give your signature a name and content. Then, set it as your default signature for new messages and replies/fowards.

Outlook Desktop is the preferred email client as it let's you view all of your mailboxes in one window.

To set up a signature in Outlook Desktop, first search for Signature in the top search box:

Under "Actions", click Signature, then Signatures. This will open the Signatures and Stationary window, where you can create and enter signatures. Make sure to choose your default signature for each account.