You didn't look at the right corner.

1). First go to "MyFlyertalk" (to you top left, the opposite to "Log In/Out").
2). Use "Edit Your Details" tab to you left under "Your Profile" Section.
3). You can enter as much info as humanly possible in the "Program Affiliations" field under "Additional Information" section.
4). Don't forget to "Save Changes."

That has nothing to do with your signature link, which is different feature and located at a different section. Hope this helps.

ETA:
I now see what you mean by the yellow pencil icon. If you click any of the pencil icons, you'll be able to edit the field you just click. After the click, you will also see both "Save" & "Cancel" options to the right of the field.

I assume you meant your FT handle by your "ID." Unless you mean something else, above are the two ways that I know of for entering/editing one's own profile/info on FT.