For English usage of verbs see the wiki article English verbs.
In syntax, a verb is a word (part of speech) that usually denotes an action (bring, read), an occurrence (decompose, glitter), or a state of being (exist, stand). Depending on the language, a verb may vary in form according to many factors, possibly including its tense, aspect, mood and voice. It may also agree with the person, gender, and/or number of some of its arguments (subject, object, etc.).
It is impossible to have verbs with zero valency. Weather verbs are often impersonal (subjectless) in null-subject languages like Spanish, where the verb llueve means "It rains". In English, they require a dummy pronoun, and therefore formally have a valency of 1.
The intransitive and transitive are typical, but the impersonal and objective are somewhat different from the norm. In this sense you can see that a verb is a person, place, or thing. In the objective the verb takes an object but no subject, the nonreferent subject in some uses may be marked in the verb by an incorporated dummy pronoun similar to the English weather verb (see below). Impersonal verbs take neither subject nor object, as with other null subject languages, but again the verb may show incorporated dummy pronouns despite the lack of subject and object phrases. Tlingit lacks a ditransitive, so the indirect object is described by a separate, extraposed clause.
English verbs are often flexible with regard to valency. A transitive verb can often drop its object and become intransitive; or an intransitive verb can take an object and become transitive. Compare:
In the first example, the verb move has no grammatical object. (In this case, there may be an object understood - the subject (I/myself). The verb is then possibly reflexive, rather than intransitive); in the second the subject and object are distinct. The verb has a different valency, but the form remains exactly the same.
In many languages other than English, such valency changes are not possible like this; the verb must instead be inflected for voice in order to change the valency.
A copula is a word that is used to describe its subject, or to equate or liken the subject with its predicate. In many languages, copulas are a special kind of verb, sometimes called copulative verbs or linking verbs.
Because copulas do not describe actions being performed, they are usually analyzed outside the transitive/intransitive distinction. The most basic copula in English is to be; there are others (remain, seem, grow, become, etc.).
Some languages (the Semitic and Slavic families, Chinese, Sanskrit, and others) can omit or do not have the simple copula equivalent of "to be", especially in the present tense. In these languages a noun and adjective pair (or two nouns) can constitute a complete sentence. This construction is called zero copula.
Spanish inflects verbs for tense/mood/aspect and they agree in person and number (but not gender) with the subject. Japanese, in turn, inflects verbs for many more categories, but shows absolutely no agreement with the subject. Basque, Georgian, and some other languages, have polypersonal agreement: the verb agrees with the subject, the direct object and even the secondary object if present.