Yo is a subject pronoun - it used when "I" is the subject (actor) of the sentence, as in this case "Yo quiero".
Me is an object pronoun, used when "I/me" is the direct or indirect object (person to whom the action is being done). For example:
(Yo) digo -- I say
(Tú) me dices -- You say to me, You tell me
(Yo) me baño -- I wash myself (me is a reflexive object pronoun here).
So:
a) Subject
I speak Spanish.
Yo hablo español.
b) indirect object
Ana sent me a letter.
Ana me envió una carta.
c) direct object
Juan paid me.
Juan me pagó.
d) reflexive pronoun:
Yo me miré en el espejo.
I looked at myself in the mirror.
"Yo" is sometimes translated as "me." For example: Soy yo. = It is me or Like me= como yo.
P.s. Me gusta (I like) - literally, it pleases me. Just a different way of phrasing the sentence.
"Debo irme" - irse can be a reflexive verb, usually used in this way when it's not followed by a complement of place.
I hope I could be helpful, if you have any doubt about what I said, send me a message! I will be glad to answer you :)