The key elements that make a sentence grammatically correct are its completeness, proper punctuation, agreement between subject and verb, agreement between pronouns and their referents, and correct use of verb form. Two of the most common errors involve the sentence fragment and the run-on sentence.
A sentence fragment does not express a complete thought. A sentence must have a subject and a verb, even if one of them is implicit. A run-on sentence contains more than one complete thought and is not punctuated correctly, either having a comma where a period is necessary or lacking punctuation. Subjects and verbs must agree in number, as must pronouns and the words to which they refer. The correct verb form is necessary for the sentence to be grammatically correct as well.