I suppose you were learning about 'verbos pronominales'1, those verb end in se, eg. laver*se*, llamar*se*, ir*se* etc.
eg. 1: I wash myself = (Yo) me lavo
The verb is lavarse
Who/what is washing? I wash: yo lavo
Who/what am I washing? Myself/me: me
eg. 2: You help me = (Tu) me ayudas
The verb is ayudarse
Who/what is helping? You help: tu ayudas
Who/what are you helping? Me: me
eg. 3: I fall = (Yo) me caigo"
The verb in this case is caerse, not caer. In English the verb is 'to fall', in Spanish it would be 'to fall myself'. Sounds strange, and don't border to much, you'll get used to it very soon.
Who is falling? I fall: Yo caigo
Who am I falling? Myself: me... this sounds strange, but for sure I don't fall someone else ;)
eg. 4: You are called Stanford = (Tu) te llamas Stanford
The verb is llamarse, not llamar. Here literal translation to English becomes even more difficult. It would be something like 'to call/name yourself'.
The verb 'llamar' means to phone someone or to ask someone to come closer (which you can also translate by call, but it has another meaning). Saying "¿Cómo tu llamas?" could mean something like "How do you make phone-calls?"
Who is calling: You call: Tú llamas
You are calling yourself: te
The rule I recommend you is to check if the verb ends with -se. Then you know you have to use an extra personal pronoun (me, te, ...).
For sure, when English version contains something like: me, you (not as subject), us, myself, yourself... it is also translated by one of those little words (I made a small list your professor probably gave you:
Pronoun as a subject (sujeto)
The equivalent (in)direct objects or objetos (in)directos