Commas are used to separate extra parts of a sentence, called clauses by English teachers. They make a long complex sentence easier to read. There are pages of long detailed rules governing this use of commas. However they can be summarised as:
1. The comma must split a full sentence off from an extra part.
2. These commas are optional; use one if it makes the meaning easier to understand.
In these examples, the part that is not a full sentence is underlined:
I first met her in Tsim Sha Tsui, where I used to work.
People, who know their manners, should give their MTR seat to the elderly.
If you remove the extra part the sentence still makes sense, but the sentence is better with the extra part added.
A comma splice is used when two sentences are joined by a comma. This joining is called an error by many English teachers, but it is used by respectable authors. It seems unfair that a structure used by good writers is wrong for the rest of us. An example of the comma splice is this sentence from the Bible, "His word is a rod that strikes the ruthless, his sentences bring death to the wicked." Isaiah 11:4 (Jerusalem Bible) Both sides of the comma splice could be sentences on their own, but the writer decided that it communicates the idea better as one sentence. The purpose of writing is to communicate not to follow rules.
The comma splice can easily be replaced with a full stop, a semicolon or in this example the word 'and'. So why is the comma used at all?
Comma splices are sometimes a better choice for joining short sentences with the same topic and structure. 'I came, I sat, I wrote the test!' is better than 'I came and I sat and I wrote the test!'
If both sides are full sentences use a semicolon (;) or a full stop (.), whichever is easier to understand. Use a comma to join sentences if you think the sentence really looks better that way and ignore the punctuation rules that say it is an error.
Next week I'll give you simplified rules for commas in quotations.