We use Team Foundation Server for our main project. Every time we add a new employee either onsite or offsite we always have to set up the references manually.
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Nothing to do with TFS, really. You just have to check in your dependencies to source control.
In your solution, add a folder called "Dependencies". Add a matching folder on disk in the same location in your solution hierarchy (annoying, I know). Add your dependent external DLLs to that directory.
As these are now part of the solution, they will travel with the solution into source control.
Reference these in your projects. It will look like this
but it should be recorded in your solution file as a relative path.
<Reference Include="Example">
<HintPath>..\..\..\Dependencies\Example.DLL</HintPath>
</Reference>
If you're having problems with this not being the case, you can simply edit your project file and change the hint path.