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.
I'm going to assume you mean "workspace", not "workstation", as your question doesn't quite make sense to me otherwise.
In Visual Studio, go to the Source Control Explorer (View->Other Windows->Source Control Explorer). At the top of the source control explorer window you should have a toolbar with a few buttons. Somewhere on that toolbar (for me it's at the right) there should be a Workspace dropdown. Just select the workspace you want to use from that dropdown.