Learn Portuguese (Portugal): Eu só falo português.

The word só can mean 'alone' when used to describe a person. However, it is very often used as an adverb meaning 'only' or 'just', as it is here. You could also use the word apenas in this sentence to mean the exact same thing.

Since this lesson is about negative words, how would I express a similar idea like 'I do not speak anything' using what we are learning?

You would use a double negative and say Eu não falo nada. In Portuguese, you must put não before the verb, but you still need the negative word nada (meaning 'nothing' or 'anything') after the verb to complete the meaning.