I don't know much about ColdFusion yet. If I declare/cfset a variable inside a function, can I just access that variable directly from anywhere on the .CFM page?
If you set a variable in a function without specifying var then yes, the variable will become globally accessible.
As Eddie said, if you don't specify "var myVariable" (or, alternatively if on CF9+, "local.myVariable"), than the variable is globally accessible. However, this is generally to be avoided as it breaks the principle of encapsulation. Generally, a function shouldn't pollute the environment around it. And not scoping variables to remain local to a function can result in race conditions or unintended behavior.