How does media manage to co-host a show from two continents without latency?
There are two key ways to deal with the inevitable latency of live video from the other side of the world:


Ignore the video, at least for talent or guest queuing purposes. The person is fed mix-minus audio through their IFB. Since it is just audio, and historically was sent over a POTS telephone line, it can have virtually unnoticeable latency to the viewer.
Practice, practice, practice. For geographically separated anchors, they will rehearse until they can get the timing of things right. They'll know they need to start talking just that little bit early for it to be seamless to the viewer.


Other technical things that can be done are to rely on terrestrial (fiber optic) transmission of the remote location (significantly lower latency than satellite, but physics still prevents zero latency) and avoiding compression or using codecs designed for low latency and high quality.