If you’re using an ellipsis to show a pause in speech, an unfinished thought or an enigmatic trailing off into silence... then you don’t need a space before it. So:
Nats asked us to gather at one end of the office. ‘That’s all I’m saying...’ she ended cryptically.
But if you’re using an ellipsis to show that something’s missing you do need a space before and after. Like:
The feedback was excellent – here’s some of what they said: ‘Please pass our thanks on to the team … you’ve made it a million times better and we think it’s brilliant.’
If the ellipsis is at the end of a sentence, you don’t need to put a full stop after it. Because it doesn’t look very good.
Beware: Padders hates ellipses.
Interesting fact: When you use an ellipsis to deliberately leave a thought unfinished in a piece of writing, it’s called aposiopesis.