The first thing to know is the different parts of speech and how to use them. A noun is a person, place or thing and is likely to be the subject or object in a sentence. A pronoun is used in place of a noun. It can also be the subject or object in a sentence, but there are some rules. If the masculine pronoun is the subject, you'll want to use "he," but if it's an object, "him" is the appropriate version to use. An adjective describes a noun, and an adverb modifies a verb (often but not always an "-ly" word). A preposition shows the relationship of a noun to another word (most often another noun). "Under," "over," "in" and "through" are all prepositions.
There are many varieties of sentence structure. The most common one is the simple sentence with a subject, verb and object. A compound sentence is the conjoining of two sentences with a conjunction, such as "and," "but" or "or," or an adverb such as "however." A complex sentence has a dependent clause joined to an independent clause. An example of this is, "Although John was exhausted at the end of a busy day, he liked to relax by chopping wood in the forest." The phrase in front of the comma is dependent on the second half of the sentence, which is independent.
A run-on sentence is one that should be made into two or more sentences because it contains more than one thought or concept. A sentence fragment is an incomplete sentence because it lacks a subject or verb. However, in some cases when the subject is implied, it would be a complete sentence.
Most of the time, the subject and verb should agree in number. If the subject is singular, then the verb should be the singular form. For a plural subject, you'll need a plural verb for them to be in agreement. For example, "John sings," while "John and Matthew sing."
There are thousands of rules in English involving conjugation, punctuation, possessive, plural possessive, passive verbs, active verbs and many others. One good resource for people who need help with their writing and grammar skills is "The Elements of Style," by Strunk and White. For magazine and newspaper writers, the "AP Stylebook" is the final word, and the "Chicago Manual of Style" is used by book authors and publishers.