If you're omitting material between sentences, use the final punctuation of the first sentence, followed by a space, three ellipsis points, another space, and then the next sentence.

"Dearly beloved, we are gathered here to honor the memory of our distinguished mayor and haberdasher, Al Goner. . . . May he rest in peace."

If the original sentence ended with a question mark or exclamation point, use that punctuation instead of a period, followed by the ellipsis points. The ellipsis points retain one space on either side.

"Do you, Melvin, take Clara to be your wedded wife? . . . I now pronounce you man and wife."

You can also use ellipsis points to indicate a pause:

"I think . . . I'm not sure . . . I believe I left the gun on the hall table."