Okay, for everyone who doesn't understand how the Offline Mode works, here's the down and dirty.
These are the Rules at least, as far as I've discerned them:
1) Thou Shalt Be Online Beforehand
2) Any game you want to play must be done updating. If it's updating when you switch to offline mode, you cannot play it because it cannot update.
3) Remember that games which use Steam Cloud for saves are no longer going to have saved games when you go offline. Also, any progress you make offline doesn't count towards any achievements, and will either overwrite or be overwritten by Steam Cloud when you go online. It depends from game to game so be careful and when in doubt just don't play it.
4)Some games will not play when in offline mode because they need to access Valve's servers for stuff. This could have a number of reasons, though that's not important really because the bottom line is that the game needs something from Valve's server that it's not able to get. This will most likely fix itself if you go back to step 1 and wait a bit. If this is unexpected internet blackout time, then my condolences to you.
5) Go to the login screen.
6) CHECK THE BOX THAT SAYS 'Remember Me' OR FORGET ABOUT OFFLINE MODE
-What this does is it saves your credentials. Steam connects to the master servers to gather your CD Keys. I mean, literally, it uses CD Keys. You can go into your program files and try to run the application '[game name here].exe' and it'll either take you to an install screen or ask you for your CD Key. Steam checks to see what CD Keys are associated with your account, gathers them, and when you run a game it plugs the CD Key in* and lets you play. The only other thing it does is the Steam Overlay. Everything else is the game as you would have it on disc.
- It is important to note that the credentials will not last forever. I've never personally been offline that long, but I've heard from a few people that the steam credentials, even when saved, are not saved forever.
7) Never, *ever* exit Steam or log out when you don't have access to the internet. Doing so wipes the stored user info, which means you just deleted your CD Keys. You'll have to log in again in order to get the CD Keys back, and that requires internet. You deserve to be without games if you disobey rule number 7.
8) Catastrophic Internet Loss causes everything to be sketchy, so play it by ear when you lose all your internets. Choosing to go offline may prompt you to log in again, meaning your stored info was just wiped. Not choosing to go offline may result in your games trying to connect to Valve Servers they can't reach and becoming unplayable. I believe that a window will pop up that has a bunch of text about not having connection and your options are "Retry" and "Start in Offline Mode". If you were smart and you told your computer to remember you, you may click "Start in Offline Mode" and you will be able to play the games that your computer has stored the CD Keys for.
And that's pretty much it. You have to be online before you can go offline. It's not that crazy when you think about it, since you have to be online to buy or download your games. At your login screen you MUST remember to click "Remember Me", so that it saves your identity to your hard drive. Then, even in the event of catastrophic internet loss, your computer still knows you and has your CD Keys. It will save this information for a limited time, but that time will be renewed when you go online. Your computer will attempt to automatically log in the account that it remembers every time you turn it on. If it can't access the internet, it uses the locally stored user info. If it can access the internet, it updates the stored user info when you log in.
*Key(s) refers to games which actually have CD Keys. Some games don't, and therefore if you can't run things through steam you may be able to just run them through your program files. There are generally few of these games, so as long as you follow all the above rules you won't see a difference and won't have to worry about file directories. Free to Play games don't have keys, but you're an idiot if you think you're going to play 'Champions ONLINE' while running Steam in offline mode.
PS. If you're a dirty cheating bastard, you can follow these rules to run LAN games with a single copy of a third party game**. Not that you should do that, because that would make you a cheap jerk. And also, I think that might kind of sort of be piracy, which is bad and that means that I cannot advocate it without a moderator besmirching my good internet name.
**Also, both computers need to have internet connections, be on the same network, and some game developers are smarter than you and will check for your account's online status and will turn off multiplayer portions when you run Steam in offline mode. So there's no guarantee that the workaround will work for you incorrigible tightwads.