I usually just buy carnets but does the Navigo pass for zones 1-6 also cover the RER as well as suburban trains? If it does, do we just get on a train and show the pass or do we show the pass at the ticket window/machine and get a ticket with it? Does it cover going to Chartes? I understand that we can use them to get Velib bikes now as well. We will be in Paris for 12 days so it may work out better for us.
An excellent and very thorough resource for all such questions is parisbytrain.com
A zone 1-6 Navigo pass will cover the RER and SNCF suburban trains in those zones. However, Chartres is well beyond zone 6 so your pass won't cover you all the way. If you want to visit Fontainebleau, it will get you there.
Navigo passes nowadays are on a machine-readable credit-card type ticket - you might occasionally have to show them on the train but it's more usual to have to touch them to machine-readable gates entering or leaving the platform.
Les Passes Navigo are fantastic to use! You don't even have to remove the card from your day bag. Just wave it somewhere in the vacinity of the big purple circle on the turnstiles, it sounds a loud "ching" and lets you pass. Be sure to take a 1" photograph to attach to your Navigo, since they are a personalized transportaion ID.