My question is very basic/dumb. What impact does assigning a city to a shared project (e.g., a wonder) have on that city's production? Does the city contribute x% of its production to the project? Does all other production stop in that city until the shared project is completed? I feel like I should be able to figure this out, but I can't. Apologies if answer can be found elsewhere. I couldn't find an answer. 

The city send all its industry towards building the project, so all other stuff the city was building is halted while it is building the project.

Thanks!

Shared projects are the same as building districts, units or infrastructure with the exception that several cities can work on the same project to speed it up.  This way you are able to spread out some districts like the Holy Sites so any city can profit from it's bonus.

In Civ, you would never build a Wonder in a weak production city, since it takes so long. Here it is possible.

You can also remove a city from the project if necessary.