E.A.
You have an account with Hulu, with a log in and password. That's what you use when you want to log in on different devices. For our PS3 and Blueray player, there's already a Hulu icon in the menu. You click on it, it takes you to hulu, and you log in there, just like logging into facebook or anywhere else. Our devices save our info after the first time, so we don't have to log in every time.
Hulu streams current shows in one of two ways - either they release the episodes a day after they air on regular tv (new shows) and you can watch them anytime after that, or they release the whole show at once (typically older ones, but sometimes if they produce it they will release a whole season at a time).
You want to watch a new show so, when you sign into Hulu, search for the show and it will give you all of the info you need about it. Hulu produced 11.22.63 but it looks like they are only releasing one episode a week. Sometimes they do that. You have to check each show individually to see what the release dates are for the episodes, the "rules" are different for each one.
I suggest choosing shows for your List online on a computer, the site is easier to search that way. Once you start watching shows, they will add them to a dynamic list that keeps track of what you watch and tells you when there's a new episode available.
I hope that helps :)