Learn Croatian: Danas ne idem pješice, čekam taksi. - Today I am not going on foot, I am waiting for a taxi.

The verb for "to go" is ići, and its "I" form is idem. To make it negative, you simply put the word ne in front of it: ne idem (I am not going). Unlike the verb "to be" which merges with "not" (like nisam), regular verbs of motion keep ne as a separate word.

Is pješice a noun that has changed its ending here?

No, pješice is an adverb meaning "on foot", so it never changes its shape. You will very commonly see it paired with ići to specify how you are moving, rather than just where you are going.

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

In Croatian, the subject pronoun is usually dropped because the verb endings already tell us who is doing the action. Both idem (I go) and čekam (I wait) end in -m, which is the standard present tense ending for "I".

The English translation says "waiting for a taxi", but I don't see a word for "for" in Croatian. Why?

The Croatian verb čekati (to wait) directly takes the thing you are waiting for as an object, without needing an extra preposition like "for". So you literally say "I am waiting a taxi" (čekam taksi).