The ellipsis (plural "ellipses") is an often-used, but rarely understood form of punctuation used in casual writing. In formal writing, the ellipsis is used exclusively to indicate that a portion of quoted material has been omitted from the quotation; in casual writing, it can have far more varied uses. The most common usage of ellipses in casual writing, however, is to act as a pause or "drifting off" of speech or thought, though it is also often used to show an omission of some information.
Errors in its usage as punctuation, then, often come from a misunderstanding of how to properly use ellipses to begin or end sentences. In the middle of a sentence, an ellipsis functions almost identically to a comma: it is attached, without spacing, to the word which precedes it, and a space is used after the punctuation.
For example... this sentence demonstrates how to use an ellipsis in mid-sentence.
As previously stated, usage of ellipsis in this form creates a natural pause that lasts longer than that of a comma, and the two forms of punctuation may be used interchangeably in this context to create the desired effect; remember that overuse of the ellipsis is highly discouraged, however.
When an ellipsis begins a sentence, though, the rules may change. This, however, is a matter of style, and whatever is most comfortable to you is recommended; simply remember to maintain a consistent style. The two most common styles are presented for example here:
...this is an example of an ellipsis beginning a sentence.
... this is another example.
Note that using an ellipsis to begin a sentence is highly discouraged and frowned-upon by many editors. In most cases, you will want to use an ellipsis to open a sentence only when the preceding sentence was ended with an ellipsis to show its natural progression.
When an ellipsis ends a sentence, the recommended style is to append the appropriate punctuation to the end of the ellipsis. Again, many styles vary in their approach to this. Below are two examples of common styles used to end a sentence with an ellipsis:
This sentence ends in an ellipsis....
This sentence ends in an ellipsis, too... .
As does this sentence fragment...!