Translation:I know how to play the guitar, but I do not have one.
This is how babies learn to speak; it's what I find so good about this method. Repetition helps you understand what 'naturally' goes together. In a previous course, I learned that when playing an instrument, the noun goes into the prepositional case and играть is followed by на. For games and sports, use играть в (+ accusative). But it is far easier to simply learn a few such as играть на гитаре / скрипке (violin) and играть в футбол / шахматы (chess).
The literal translation would be "but I do not have her". Nouns get replaced with a pronoun that correspond to their gender in Russian, even if they are inanimate objects. Since inanimate objects are referred to as "it" in English, that is what "её" would translate to when referring to a guitar, in context. For example: "Где твоя гитара? Я её не вижу." — "Where is your guitar? I do not see it.
And you're right, её is in the genetive case here.
It's the prepositional case, therefore the noun requires a preposition.
More examples with "играть":
- играть в футбол (activity, accusative)
- играть Чайковского (composer's name, accusative)
- играть вальс (waltz) (musical composition, accusative)
- играть с ребёнком (with a child, instrumental)
- играть на гитаре (musical instrument, prepositional)
- играть в доме (at the house, prepositional)