I'm new to italki and I've only had one language exchange, but I think what most people do is exchanging Skype addresses (I suppose other video platforms can be used, but this seems like the de facto standard) and they agree on a time. Then they videochat for an hour, half an hour in one language and the other thirty minutes in the other language.
I think that, once you get to know the other person a little bit, it's important to agree on specific topics to speak about, difficulties each person has in order to focus on those, etcetera. Otherwise the conversation can be rather empty and very beginner-like.
Speaking to strangers can also be quite overwhelming for introverts, so I think it's better if you get to know each other a little bit via chat first.