How do I add a new product tag in a program?

highlight the tag you want to add a new value first, then at the top of the tag section click on the 'New' pick list with the green plus sign.

Select 'New Tag Value' from that pick list. Here you can add a new value to you Product tag.

Thanks for the answer, but perhaps we are using a different version of Marketo. The only optsions I have are: New campaign folder, new smart campaign, new locat asset, new program.

You will need admin access to add a tag value.  You would go to "Tags" in Admin, then in the list, select the tag you want to edit and add the value. 

Thanks Cheryl!
The trouble with copy 'n pasting, I missed my first line in my comment.. :-)

As Cheryl stated, must be in the Admin section not in the program setup section.