Be nice to your sentences and don't splice them.
The comma splice is any easy mistake to make. I went years without knowing exactly what it was--all the way through to AP English in eleventh grade. I know I was taught what a comma splice is, but I think I overcomplicated it and confused myself. It's so simple, though, that I can't believe I never figured it out on my own.
Put simply, a comma splice occurs when you try to connect two complete sentences (more commonly--and accurately, if not understandably--called independent clauses) with only a comma. Strunk and White are not fans, to say the least. In some languages, comma splices are grammatically correct, but not English.
So how do you recognize and avoid them?
To begin, review what makes a complete sentence: a subject (a noun or noun clause) and a verb (or verb clause) that go together. The girl smiles. The cat runs. The horse neighs. Purple polka dots are bright. Now, each of these can stand alone; each is an independent clause. Commas are intended to connect dependent clauses (like prepositional phrases) to each other or to independent clauses. A comma used correctly will look like this:
When the girl smiles, the cat runs.
"When the girl smiles" has a subject and a verb, but the word "when" changes the function of the phrase to a dependent clause. Thus, the comma is place after the dependent clause and is actually necessary. However, if we dropped the word "when," then "the girl smiles" would become an independent clause, and it would be incorrect to use a comma like this:
The girl smiles, the cat runs.
This can be corrected easily with any number of changes, depending on the context. If the two independent clauses are very closely related, a semicolon (;) is generally acceptable. If the two independent clauses are connected a little more loosely, then a comma followed by the word "and" usually will suffice. Other times, a comma followed by "but," "or," or "then" is more appropriate, but some sort of conjunction is necessary. If you can't figure out which one to do, then you can simply separate the two independent clauses into two sentences with a period.
The girl smiles; the cat runs.
The girl smiles, and the cat runs.
The girl smiles, but the cat runs.
The girl smiles, then the cat runs.
The girl smiles, or the cat runs.
The girl smiles. The cat runs.
Any of these would be acceptable. Oftentimes, a comma is not used before "and" unless you are joining three independent clauses; however, I used it here for the sake of simplicity, and because either way is technically correct.