When you see three spaced "periods" in a row, you are in the presence of an ellipsis. What this means is that something has been left out--usually, a part of a direct quotation.
As you probably know, a direct quotation must be presented exactly as it is in the original. If you have to make a change in the quotation, you must signal your reader that you are making a change. The most common type of change is to include only part of the text you are quoting from. When the part omitted occurs within a single sentence of the quoted material, ellipsis is indicated by three spaced periods. For example, if you wish to quote only a part of the first sentence of this paragraph, you would do it as follows:
As you probably know, a direct quotation must be presented . . . as it is in the original.
(Of course, it would be silly to use an ellipsis just to omit one word, but even if what you are omitting is an entire clause, you would still use the ellipsis points as in the example above.)
If you have come to the end of a sentence, and what you are omitting is part of the next sentence, or one or more sentences between what you have already quoted and the point where you pick up the quotation again, then you need not only the three ellipsis points, but also a period to signal the end of the sentence. That period, like any other period, bumps right up against the sentence it ends. It is followed by a space, and then the three spaced ellipsis points. Let me use this paragraph to illustrate what I mean.
If you have come to the end of a sentence . . . then you need not only the three ellipsis points, but also a period to signal the end of the sentence. That period, like any other period, bumps right up against the sentence it ends. . . . Let me use this paragraph to illustrate what I mean.
Notice that the first ellipsis occurs within a single sentence, and consists only of the three spaced points. The second ellipsis includes the period following the word "ends." Don't forget to space also before the first ellipsis point, and after the last one.
While some writers use ellipsis points to indicate a trailing thought, that is a privilege reserved to those who have already mastered the proper use of ellipsis points. Don't use this form of punctuation as if it were merely decoration, or a funny looking version of "and so on and so forth."
Although it used to be common to use ellipsis points to signal missing words at the beginning or end of a short quotation from a work of literature, it is now common usage to dispense with all that unnecessary clutter. For example, when quoting a word or a phrase from a line of poetry, you don't have to use ellipsis points to signal that you aren't quoting the entire line. It would be perfectly acceptable to say something like this: Like Yeats' "rough beast," the new social order "lurches toward Bethlehem to be born."
Whatever else you do, though, don't use ellipsis points as if they were decorations for your prose. Writing of that sort reminds me of preteen girls who dot their "i's" with circles and hearts. It has a silly, breathless quality to it, don't you think?