Help leaky older Delta 3-handle faucet

[JMac]

I have a leaky faucet that is getting worse. I am guessing it is Delta as that is what it says on the handles. The faucet was installed anywhere from the early 70s until the mid-00s, and most likely they are original from the 70s. The only thing metal is the extension pipe; everything else is plastic. I got down to the wall nub, but didn't want to go further without 'assistance' and hopefully some idea of what I will need when I get there.
What do I use to get the plastic nub out, or do I need to remove it, or is it even removable? I am guessing the cartridge or washer that needs replaced lays just beyond this?
TIA
James

 

[hj]

That "thing" in the right hand picture IS the stem. I cannot tell if you have removed its retainer or not, (it looks like you have), but if you have it just pulls out.