Repeat after me: An ellipsis is not an em-dash… An ellipsis is not an em-dash…
Those three dots (not five or eight or however many you feel like scattering on the page because someone once told you the number of dots indicates the length of the pause — what absolute twaddle!) indicate a long pause, or a trailing off of the sentence, or something left out. An ellipsis (plural: ellipses) does not indicate an abrupt change of direction in a sentence; that’s one of the things em-dashes are for.
Also, if you begin a new thought after the one trailing off with an ellipsis, you need to treat that new sentence as, y’know, a sentence. Leave a space after the ellipsis, the same as you would with a period or question mark, and capitalize the first word of whatever follows. Even if the ellipsis only indicates a long pause, you need to add a space after it before going on, the same as you would with a comma.
Ellipses in dialogue work like this:
“And you were planning to…?” she asked.
“I don’t know…,” her house cat replied. “I could… I want to win the Fetch tournament! And I will… for Mom. To make her proud.”
See how the standard punctuation you’d use in dialogue and tags is still there, following the ellipses? If you’d use a comma, you still use a comma after the ellipsis. If it’s a question that trails off, you still use a question mark. Journalism style guides such as the Chicago Manual of Style discuss ellipses mostly in terms of how to use them in quotations, and thus they don’t have anything to say about whether to add a fourth dot — a period after the ellipsis — to the end of a trailed-off sentence. If you use that fourth dot, use it only for the end of a trailed-off sentence (one you’d end with just a period if it didn’t have that ellipse), and be consistent about it.
Update: Something I’ve seen a lot lately is the two-dot “ellipse,” supposedly for indicating a shorter pause that a real three-dot ellipse. Who [expletives deleted] is teaching writers to do this?