I have no idea how you would keep track
I can see two issues. First, how to track your own positions on open contracts. Second, how to find the open contracts to bet on.
For the first, I imagine there'd be a table UI which would list the contracts you're betting on with an indication of the current "price" and whether it's changed To keep load off the servers, maybe some kind of client app talking to a web service that exposes the data would work.
For the second, usually these web sites organize the contracts by a taxonomy, e.g. politics vs. economics vs. sports and so on. You navigate the taxonomy to find contracts of interest. Metadata like that is also useful to answer questions about track records. For example, a poster might be very good at predicting political events but bad at economics.