It seems to me that when expositing in science-fiction the risk of being obtrusive is nearly unavoidable. Likely, you’re dealing with concepts that are completely new, so exposition is required. Here are some of the strategies:
1) Find a character who, for whatever reason, doesn’t understand the way his or her world works. Perhaps, they’re a child, or they’ve been living in a cave, or they’re from another time. And then have that character ask dumb questions. You can even get some character conflict mileage out of this dynamic.
2) Each time you introduce a new concept, just launch into description — potentially the most obtrusive of the techniques.
3) Exposit through action. Show how things work as part of the action that advances the story. Just make sure not to invent sub-plots for this obvious purpose.
4) If the thing to be exposited is complicated, it would make sense to have one character teaching another how to interact with it.
5) Don’t exposit. Leave some mystery. This technique can be used along with number 3 well.
What other methods can you offer?