How does extradition take place between states?

[struggle4progress]

8. My summary (as a non-lawyer): The Constitution and Federal Statute require extradition,

but (as with other arrests), the lawfulness can be contested by habeas corpus (unless the writ be suspended for insurrection or similar threat to public safety)

I expect refusal to honor a lawful extradition request would produce a suit and subsequent order to honor it, but the lawfulness could be contested by the detainee with a habeas action; in the current context, suspension of the habeas right is unlikely to be considered or upheld