Non-finite verbs do not show tense, person, or number and include infinitives, -ing forms, and -ed forms. They cannot act as the root of an independent clause. Finite verbs agree with the subject and express mood, tense, number, and person, while non-finite verbs do not agree with the subject and are used in forms like the present participle, past participle, or infinitive. Examples of non-finite verbs are "to drive," "being ready," and "having completed," while finite verbs often include auxiliary verbs and usually follow the subject.