So, here is a tutorial I'm posting so that a) people might learn the grammatically correct way to punctuate their writing, and b) reviewers can just attatch this link to critiques instead of inventing examples of their own.
The same sentence can be written three different but correct ways.
Period + capital letter= She hurled the vase across the room. It shattered as it hit the wall.
Comma + conjunction= She hurled the vase across the room, and it shattered as it hit the wall.
Semi-colon= She hurled the vase across the room; it shattered as it hit the wall.
There are pluses to using each of these as punctuation. The period gets across a complete thought, and the reader can come to a full stop at the end of the sentence. With the comma and the conjunction (common conjunctions are 'and', 'but', and 'or') the reader can connect two thoughts together to give a smoother flow. With the semi-colon, though, they can find a happy medium by keeping the two thoughts connected yet independent.
However, here are common mistakes I come across.
While this remains correct: She hurled the vase across the room, screaming as it shattered.
This doesn't: She hurled the vase across the room, she screamed as it shattered.
Here in the second one (also called a comma splice), either 'and' needs to be added before the second 'she' or the comma needs to become a semi-colon. This is because both clauses before and after the comma are complete thoughts with a subject and a verb, and semi-colons are used to seperate two complete thoughts
If you need to know whether to put a comma or a semi-colon, try reading both parts of your sentence aloud. If they both make sense seperately and are complete with a subject and a verb in each one, you add a semi-colon in between. If not both parts make sense alone (i.e. one part doesn't have a verb or a subject) then just add a comma.

The bottom line: you need two verbs and two subjects in the sentence to use a semi-colon.
Anna sat at the picnic table; she ate her burger.
To use a comma all alone, there cannot be two verbs and two subjects.
Anna sat at the picnic table, eating her burger.
Two verbs (sat and eating) but only one subject (Anna).
Semi-colons and commas+conjuctions can be used interchangeably.
For more help:
http://owl.english.purdue.edu/handouts/grammar/g_commacomp.html
http://web.uvic.ca/wguide/Pages/GramSemi.html
If anyone still is confused about using commas, semi-colons, or even conjunctions and colons, they can PM me and I'll immediately try to assist them.
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