Some points not addressed in the above answers:
While Steam lets you create multiple libraries, it appears some games can only be installed in the primary library. I suspect this applies to games (eg, those using the Source engine like TF2) with shared content.
Using a symlink to move the
SteamApps library folder out of the
Steam directory causes problems, since some games appear for whatever reason not to follow symlinks. Certainly this TF2 bug is related, but others may also be. (It appears you can do this successfully using a bind mount, but this is unnecessary - see below).
However, to answer the original question - you can just move the
Steam folder entirely to a new location (eg, to move it to
sudo mv ~/.local/share/Steam /opt
Once it is moved, attempt to start Steam (using the Unity icon or
/usr/bin/steam). You will get a message:
Couldn't find Steam content, did you move it?
Which will let you select the new Steam directory. Subsequently it will start normally.
This worked moving Steam to another
ext4 filesystem. I do not know whether this will work if you change the permissions or attempt to use a non-linux filesystem.
I have not tried sharing a library directory between Windows and Linux steam. I suspect this would end badly.
Steam directory will usually make SteamGuard require an unlock code the next time you start Steam.