Myth: You must be online to use offline mode
Due to the Steam support article only giving instructions to use offline mode when you are already online, many people think that this is the only way to use it. Luckily, this is false, as an offline mode like this would be rather useless. If you start Steam without an internet connection you will be given the option to start in offline mode.
Fact: If you don't exit Steam manually, offline mode may not work.
Unfortunately, this may not always work due to a bug. When Steam starts in online mode, it modifies a cache file called winui.gcf. When Steam shuts down, it changes it back. However, if Steam is running whenand means the process is not given the chance to change the file backfile is not changed back. On startup, Steam detects that this cache was not shut down properly, and attempts to fix it. However, this process requires an internet connection, so if you are starting in offline mode, Steam will fail to open and will display this error message.
Myth: Offline mode works fine for me, so there isn't a problem!
Not everyone experiences this problem. I have found that on some computers, the cache file is not detected as damaged after a forced shutdown and offline mode will work normally. If you're one of these people, then you're lucky, but that doesn't mean it works fine for everyone else. Some people are also lulled into a false sense of security by testing offline mode after disconnecting from the internet. As they manually exit Steam before trying the offline mode, the cache file is shut down correctly and offline mode will work. Then when they actually need to use it, they find that it does not work.
How to ensure you can get into offline mode 100% of the time
1. Back up winui.gcf
Manually close Steam by right-clicking on the notification area icon and slecting Exit. Go into the Steam/steamapps folder and look for a file called winui.gcf. Right-click on it and select Copy, then right-click on an empty area of the folder and select Paste. This will create a file called winui - Copy.gcf. If you ever need to use offline mode and you encounter the problem, just delete the old winui.gcf file and rename the copy to winui.gcf before trying to start Steam again.
2. Exit Steam manually
As long as you remember to manually exit Steam before shutting down your PC you will always be able to use offline mode. Of course, there is always a possibility you may forget, so it is a good idea to make a backup as well as detailed above.
3. Disconnect from all networks
If you are connected to a local network, but not the internet, you may find that Steam hangs at the Updating Steam... dialog. To get around this problem, just disconnect from the network."
Credit for this post to X.nano on the Steam Forums