What's a verb? A verb is any word that expresses action or otherwise helps to make a statement.
Action Verbs: Action verbs are verbs that express action. Any word that expresses some form of action like 'run', 'sit', 'love' are action verbs. Action verbs do not have to express actions you can see. You can Love someone without anyone seeing it. Some others would be; 'think' or 'hate'.
Linking Verbs: There are two types of linking verbs, To-Be verbs and other Linking Verbs.
To-Be verbs: To-Be verbs are the different forms of the word be. These include am, were, was, are, and so on. They also can include two words like, should be, could be, would be. All To-Be verbs are either linking verbs or helping verbs (see below).
Other Linking Verbs: Other linking verbs link a noun (usually the subject) and it's adjective. For example, if I said, "The dog looked odd." I am not saying the dog looked at anything, it just looked odd. The verb looked links the noun 'dog' and it's adjective 'odd' because the dog was odd.
Linking verb notes: If you can replace the verb with the word 'equals' and the sentence still means the same thing, it's probably a linking verb. For example, If I took the sentence "The dog looked strange" and replaced the verb 'looked' with the word equals, the sentence would say "The dog equals strange". Now this sentence makes less sense, but it still means the same. It means the dog was strange.
Helping Verbs: A helping verb is part of a verb phrase. A verb phrase is a to-be verb that is mixed with an action verb. For example, we could say "The man was walking." The word 'was' in that sentence is a to-be verb. However, 'walking' is also a verb. If you find a to-be verb used with an action verb, it's a verb phrase. In a verb phrase, the to-be verb is called the Helping Verb.
Transitive/Intransitive: The difference between transitive and intransitive is the direct object. The direct object is the noun the subject does the verb to. For example, in the sentence "The dog ate the food", the subject (dog) did the verb (ate) to the direct object (food). Remember direct objects have to be nouns or pronouns. If you are looking for a direct object, find the subject first(dog). Then find out what the subject does(ate). Last find out if the subject does that verb to something else in the sentence. What did the dog eat? He ate the food, so food is the direct object.
If a sentence has a direct object, then what ever the verb is that the subject did to the direct object is transitive. If there is no direct object, it's intransitive.