> If I can't get everything done in the folder that day, does the stuff get moved to the next day?
No, it just shows up like something new in your inbox. For each thing, you decide what needs doing. If it's a reminder to act (e.g., "book sale starts today") it might kick off action (e.g., "errands: drop by book store"). Another might be a waiting for reminder (e.g., "2 weeks since Bob promised report - done?"), which might kick off a follow-up contact.
Generally, carrying forward like you suggest is a big red flag in my book. It's one of the fundamental philosophical differences between Allen's thinking (one master action list, and specific constrained use of the calendar), and the "schedule everything, but roll unfinished work forward" approach more popular in other systems, and in the past.
(Side note: I recall a few months ago a cryptic news item from David Allen about moving in the latter direction, with some caveats re: rolling forward, etc. Anyone heard more about that? Or is that part of the new book...? Inquiring Minds want To Know!)
> and what goes into the folders? action lists and projects?
There are a few classes of things - reminders, mainly. Examples:claim checks, deadlines, milestones, w/f, etc. (I'd like to see a tight, small list of categories if anyone has this...)