<p>I have multiple projects in a couple of different workspaces. However, it seems like I can never figure out how to change my current workspace. The result is that files that I have checked out on my machine are shown to be checked out by somebody else and are not accessible.</p>

I don't entirely understand your question.
Are you saying that files you check out on one machine seems to be unaccessible on another of your machines? I'd say that would be entirely by design, as now you have a file that has local modifications done on one machine, which may or may not be available on your other machines.
When you say
checked out by somebody else
, what does that mean exactly? How are you verifying this, what are you looking at?
Or do you mean something else? In that case, please elaborate.