"You learn Esperanto quickly!"
Translation:Vi lernas Esperanton rapide!
So the fact that 'vi' is the subject makes it 'EsperantoN' rather than just plain 'Esperanto'?
My linguistics never was up to much!
No. Because the verb "Lernas" is referring to Esperanto, you add -n at the end. (What exactly are you learning? You are learning Esperanto) This happens with all verbs except for "Estas".
If it is the subject, it uses the default ending but if it is the object of the sentence you have to add the letter n. This is true of all nouns and adjectives in Esperanto.
Here is an example:
Esperanto estas bela
Esperanto is the subject, so it ends with o
Mi lernas Esperanton
I am the subject, so Esperanto gets n