If you tap the pen icon, you should be prompted with a list of saved signatures to choose from to add. If you always want a signature included when composing emails from a given account, go to Settings/(chosen) Account / Signatures where you can configure different signature options.
As for the other instructions.
When I go there I see the 4 options. They each say None. If I click on them the screen changes each says None and have a check mark.
Not sure how to change this.
Did you manage to create and save some signatures under Settings/Signatures? From your first post it sounds like you couldn’t save them, in which case there is nothing to select from when composing an email or associating signatures to accounts.