Login to AOL Mail

Click on "Settings" on the Top Right
 

Click on "Compose" in the Left Panel
 

On the Right, you will a Signature option
 

Click on the option which shows "No Signature" by default
 

Select "Use Signature"
 

Enter your signature and click the check box "Automatically add email addresses to Contacts" and then click "Save".

Create a new AOL email message to check your signature. Your signature should appear automatically every time you open a new message.