Exposition in dialogue

The task when writing expository dialogue is to make it interesting enough not to lose the audience, as you would do by having some character just stating the facts. Often you try to wrap these facts in some kind of dramatic situation. There you can pass on the the necessary information without thew audience noticing, as their attention is focused on the drama.
Another trick is to withhold the information by creating a reluctance in the character who is to deliver what you want the audience to know. If this character is asked to explain something but refuses, the audience will get curious. This way the exposition will be satisfying, as you have created a need to know.
In this movie clip from Aliens (1986 © FOX) you see this kind of dynamics played out when Burke realizes Ripley does not know for how long she has been in hypersleep.