Comma Splices & Fused Sentences:

You create a comma splice when you connect two independent clauses with only a comma. You create a fused sentence when you run two sentences together without any punctuation. 

Example of a comma splice: I walked to the old schoolhouse on the corner, it was not like the one I remembered from my childhood.

You cannot connect two independent clauses with only a comma.

Example of a fused sentence: I walked to the old schoolhouse on the corner it was not like the one I remember from my childhood.

You cannot “fuse” two independent clauses together.

 How to correct comma splices and fused sentences: 

a)     I walked to the old schoolhouse on the corner; it was not like the one I remembered from my childhood. (Connect with a semicolon if the clauses are closely related)

b)     I walked to the old schoolhouse on the corner, but it was not like the one I remembered from my childhood. (Insert one of the seven coordinating conjunctions after the comma. The coordinating conjunctions are “for, and, nor, but, or, yet, so.”)

c)      When I walked to the old schoolhouse on the corner, it was not like the one I remembered from my childhood. (Make one clause a dependent (or subordinate) clause by adding a subordinating conjunction, for example, “when, because, after, since, before,” etc.)

d)     I walked to the old schoolhouse on the corner. It was not like the one I remembered from my childhood. (Insert a period between the clauses and make two distinct sentences)

e)     I walked to the old schoolhouse on the corner; however, it was not like the one I remembered from my childhood. (Connect the sentences with a conjunctive adverb (however, nevertheless, consequently, subsequently, on the other hand, moreover,” etc. When you use a conjunctive adverb, it is preceded by a semicolon and followed by a comma.)

Fragments
A fragment is part of sentence and does not express a complete thought. 

Examples:

1)     Which is what I should have done in the first place. (Adjectival clause)

 Correction:

a.      I changed the lock on the door, which is what I should have done in the first place.

2)     Something that she later regretted.   (Adjectival clause)

 Correction:

a.      Susan ate the entire cake, something that she later regretted.

b.      It was something that she later regretted.

3)     Looking over his shoulder and taking deep breaths.  (Participle phrase)

 Correction:

a.      Looking over his shoulder and taking deep breaths, John walked through the dark alley. 

b.      John was looking over his should and taking deep breaths as he walked through the dark alley.

4)     Because I wanted to be his friend. (Dependent or subordinate clause)

Correction:

a.      I made an overture to John because I wanted to be his friend.

b.      Because I wanted to be his friend, I made an overture to John.

5)     First, the ten rules of comma usage. (A noun phrase)

Correction:

a.      First, the ten rules of comma usage will be covered during the semester. 

b.      First, the ten rules of comma usage are important for every writer to know.

c.      First, we will address the ten rules of comma usage.