Me llamo Ana. ¿Y tú? My name is Ana. And you?

Me llamo: "my name is"

• Me llamo Ana is word for word "I call myself Ana". The little word before the verb shows who it's about: me is about me, se is about him, her or a person you call usted.

Soy, eres, es: the verb "to be"

• Yo soy Pablo, ¿Eres estudiante también?, Y ella es Ana: soy is about yourself (I am), eres is about the person you call tú (you are), es is about him or her (he is, she is).
• ¿De dónde eres, Ana? means "Where are you from, Ana?", No soy de España means "I'm not from Spain": de means "from".

Where did "I" and "you" go?

• No soy de España, pero vivo en Madrid, ¿Hablas español?: there's no word for "I" or "you" here. The verb ending shows who it is: vivo, hablo (ending in -o) mean "I", hablas (ending in -as) means "you".
• Yo soy de Sevilla: Pablo adds yo for contrast, the way you'd stress "I" in English: "Well, I'm from Seville."

Informal and formal you

• Ana and Pablo use tú with each other: ¿Y tú?. The teacher uses usted with Pablo. With usted the verb has the same form as for "he" or "she": se llama.

Encantada, la profesora: feminine forms

• Mucho gusto and Encantada both mean "nice to meet you". Ana is a woman, so she says encantada with -a at the end; a man would say encantado.
• Soy Marta, la profesora: la is the feminine word for "the". In ¿Y el apellido, Ana?, el is the same word for a masculine noun; English says "your last name" here.