There are three kinds of connecting words that can link two sentences: conjunctions, subordinators, and logical connectors. Conjunctions include FANBOYS words like "for", "and", "nor", and "but". Subordinators introduce dependent clauses and include words like "because", "if", and "although". Logical connectors are used more in writing and include words like "however", "therefore", and "consequently". The document provides examples of how to use commas with each type of connecting word.