Nouns are an open class of words (new verbs come into the language continuously). There are subsets of verbs, though, like auxiliaries and modals, that are for the most part closed classes.
In the standard English verb phrase, the elements must follow a strict sequence: modal + perfect "have" + progressive "be" + passive "be" + main: The Seahawks should have been being beaten by the Broncos at halftime. Obviously not all VPs are modal perfect progressive passives, but the order remains the same no matter how many elements are present.
INFLECTION: Verbs have a "bare form," and then inflect in the third person singular, the simple past; the -ing participle, and the -ed participle (I walk, she walks, you walked; walking, walked). The verb "be" has a more elaborate conjugation, and is one of the few verbs that also has "irrealis" (if I were you) and is used in the subjunctive (be that as it may)
Verb phrases are characterized by several features that interact to form specific meanings and uses:
MODALITY. A verb phrase may be introduced by a modal verb that must come first in the phrase; in Standard English, only one modal verb can be used per VP. Common modals are shall, should, can, could, will, would, may, might, ought to, need to, must, have got to, used to. Modal verbs can be used as operators (see below). They are "defective" in that they inflect for tense only, not for number or person; they lack participles. Modal verbs indicate wishes, possibilities, attitudes, recommendations, and other nuances that speakers add to main verbs:
ASPECT. English aspects include simple, progressive, and perfect. The progressive and perfect can be used together. Aspect is primarily concerned with whether the verb action is habitual, ongoing, or over with. The progressive is formed by the auxiliary "be" followed by the -ing participle. The perfect is formed by the auxiliary "have" followed by the -ed participle. The perfect progressive is formed by the auxiliary "have," the auxiliary "been," and the -ing participle. The tense of the first auxiliary in the VP gives the tense of the phrase. For example:
MOOD. Most English sentences are in the indicative mood. Specialized alternative moods are the irrealis and subjunctive (see the verb "be" above, and "frozen" subjunctive expressions like "so help me God" and "thy kingdom come"); and the imperative, which is formed with the bare form of the verb (and a second-person subject usually understood). Eat your kibbles! Watch out for that cat! Pour the water in the bowl!
VOICE in English can be active or passive. Passive VPs are formed by using the "be" auxiliary with the -ed participle. Passive VPs can be in different tenses and aspects: I am shocked by my cat's behavior. Whisper is being watched by a suspicious neighbor. Whisper was scared by the dog. I was surprised by the storm. I have been amused by cats. I had been forced by circumstances to sell Whisper.
TENSE in English can be past, present, or future, but only past and present are truly inflected (see inflection, above, and also aspect and voice, for examples of past and present). Future must be indicated by various additional means:
FUNCTION: Two important uses of verb phrases come in interrogative and negative sentences. Linguists sometimes see these two kinds of VPs as separate moods, but since they have to do more with the use of sentences in conversation, and the way verbs are surrounded by small grammatical words (particles and operators), it also makes sense to see them as just ways in which the standard features above are adapted to different uses and situations.
Function is often indicated by operators, which include the modal verbs, but more commonly and importantly the operator "do." Operators are involved in four major functions that are often associated with the acronym NICE:
NEGATION: You don't have a cat. I do not give my cat baths. She doesn't like cats. Whisper didn't catch a bird today. Whisper won't take his medicine.
INTERROGATION: Do you ride your horse? Did you go to the races? Don't you just love horse racing? Shouldn't we let our horse rest?
CODE: She doesn't have a cat. I do. She keeps snakes as pets. I don't. I have a wonderful cat. Do you? I might get a cat. You might too.
EMPHASIS: I did give the cat some food. You do help out with the litterbox.
English has many multi-word verbs, consisting of verb + one or two particles. The meaning of these verbs is heavily idiomatic. When intransitive, or used intransitively, these verbs look alike: My hangover wore off. Whisper turned up. My flight takes off at ten. Let's hang out this weekend. Hang on while I get my jacket. Ken worked out at the gym. Their plans worked out.
When transitive, these verbs break into two clearly-defined classes: "phrasal verbs" where the particle can be moved to the other side of the object, and "prepositional verbs" where they cannot.
PHRASAL VERBS: I cheered Doris up. I worked their problems out. I picked the dry-cleaning up. Putin took his shirt off. I looked the information up online.
PREPOSITIONAL VERBS: I looked at my phone. I got off the bus. Whisper came across a lizard. I decided on a good recipe for Thanksgiving. I kept up with the Joneses. Watch out for that bus!
Note that the meanings of the phrasal verbs change, or disappear, if the particle is removed. Note that the prepositional verbs are not followed by a prepositional phrase. Or if they would be, the meaning would change. You can look "at a phone" in the sense of glancing at it as you would anything. But you "look at" a phone in the sense of consulting it, or reading information from it. There are (as always) several different ways of classifying such verbs. Commnet.edu has an interesting chart that offers some refinements and examples.