First of all, most people learning dead languages aren't learning to speak, they're learning to study anthropology, literature, history, or some other field that doesn't require speaking the language.
Even so, someone may want to learn to speak a dead language, even if it's not directly related to their immediate reason for needing to learn it.
And learning to speak without native speakers available can be a handy skill for living languages too, as you may not live in an area with people who are able or willing to help you practice.
Get some spoken examples
Of course the first key to learning pronunciation when you don't have native speakers is to find samples of the spoken language. For dead languages, these may need to be constructed (by you, or someone else), but you'll need them regardless. Learning to speak is the act of mimicking other speakers, so you can only succeed up to the point that you have material to mimic!
Depending on how many (if any) speakers there are of your target language, you may have success finding movies, music, or other mass media in the language. You may also find resources like RhinoSpike and Forvo useful.
Speak to yourself
Once you have some other spoken material, listen to it, and practice speaking to yourself out loud. In the early stages, this may be simply reciting the recorded spoken material you've found, but as your proficiency improves, you can begin forming new sentences, grammar constructs etc.
Check your work
As you won't have native speakers near by to correct you when you make a mistake, you must be extra vigilant to check and double-check your speaking.
Do this by recording yourself speak, then comparing to your source material you acquired in step 1.