The subject is the actor of the sentence, the person or thing doing the action. The verb is the ‘doing word’, the action of the sentence. The object is the element of the sentence that is acted on, that the verb is directed towards.
A simple example:
Jenny loves painting.
“Jenny” is the subject, “loves” is the verb, and “painting” is the object.
Whilst “painting” is itself a verb, in this sentence it plays the part of the object because it is that which the verb (“loves”) is directed towards.
Most sentences are not as simple as “Jenny loves painting”, however, and will contain a number of verbs, actors and objects. In your native language, you will probably know that a sentence is incomplete, even if you cannot explain why. This is because you have grown up surrounded by that language and have absorbed its rules in practice, even if you do not know what those rules are in theory. But when you are writing sentences for an academic essay, you will probably find that you are using more complicated sentences. Thus it will help you to write correct and clear sentences if you are able to identify the main subject, verb, and object of a sentence, i.e. the essential information the sentence is conveying.
Even though she enrolled on the course because she wanted to learn print-making, it is painting that Jenny really loves.
Despite the additional information and other verbs (“enrolled”, “wanted”, “learn”), the main verb is “loves” and the main object is “painting”.
Bear in mind that the main verb may be connected to “to do”, or “to be”, which in English are irregular verbs. The different forms of “to be” are notoriously difficult – here is a helpful guide to its conjugations.
If a sentence does not have a subject or a complete main verb, then it is grammatically incorrect. Your word-processing software may underline it in green and say “Fragment (consider revising)”!
Art of all kinds on display.
This can be made correct by completing the verb: “Art of all kinds was on display”, or by changing “art of all kinds” from the subject to the object by adding a subject: “I saw art of all kinds on display”.
A common grammatical error is subject-verb disagreement, when plural subjects take a singular verb and vice versa. Even first language English speakers may make mistakes in sentences with multiple clauses (see below) or those with compound subjects (i.e. “Jenny and her friends”): here is a US university’s guide to getting it right. You may also struggle with consistency of verb tenses, i.e. making sure that the present, past or future tense of a verb is consistent with the other verbs in the sentence. Purdue University’s resource has good advice on this.