Learn Portuguese (Portugal): Muito prazer, chamo-me Pedro.

The verb chamar means "to call". In Portuguese, to state your name, you literally say "I call myself". The -me is a reflexive pronoun that means "myself". If you just said chamo Pedro, it would mean you are shouting for or calling a person named Pedro over to you!

Why is the -me attached to the end of the verb with a hyphen?

In European Portuguese, the default rule is to attach pronouns to the end of the verb using a hyphen. This is called enclisis. This is why we write chamo-me and not me chamo (though you might hear the latter in Brazilian Portuguese).

Does Muito prazer literally translate to "Nice to meet you"?

Literally, Muito means "much" or "a lot", and prazer means "pleasure". So it directly translates to "Much pleasure", but it is the standard, everyday phrase used just like "Nice to meet you" in English when being introduced to someone.

Where is the word for "I" (eu) in this sentence?

In Portuguese, you can usually drop subject pronouns like "I" (eu) because the verb's ending changes to show who is doing the action. The -o ending in chamo already tells us it is the "I" form, making the word eu unnecessary.