This can easily be answered on Wikipedia:
https://en.wikipedia.org/wiki/Transitive_verb
See the navigation menu to the right as well for related topics (intransitive, ditransitive, etc.).

In short, how many arguments does the verb take? Sometimes it can be tricky because a verb can have multiple argument configurations. (Check your textbook for whether you're supposed to classify it twice, or classify it based on the most possible arguments, or something else.)

Verbs themselves only form the verb phrase. More complex sentences have other phrases doing other things. Or potentially other things (non-arguments) in the verb phrase like adverbs. "I walk" and "I walk frequently" use the same verb, which is intransitive in both cases, even though there's an additional adverb in the second phrase.

By the way which text book are you using? : D

He's probably using Wikipedia.