1. Know what a sentence is and remember that you don't put a comma after a sentence. A sentence has three essential components: subject, verb, and complete thought. The biggest mistake I see in student work is the notorious comma splice, where one puts a comma after a main clause: for example, It was raining, I got wet.
Maybe it may seem "artistic" to put the comma in, but technically it's wrong.
2. Another problem people have is not using the comma after the introductory phrase or clause. I often see something like this: After the storm; the sun came out. Wrong! You need a comma after storm to tell the reader that you are preceding the main clause.
3. You also need commas when listing items, for example: I went to the store and bought lettuce, tomatoes, and cheese. You need a comma between your last and second to last item (although some grammar books say you it is optional, not necessary).
There are many more rules of commas, but since you asked for just 3...that's what you get.