Once you have connected to the server, click on Source Control Explorer under your Team Explorer. From here, you will be able to clone/download your desired folders from the repository:

This will open Source Control Explorer. Select the team project from the left-side panel to view its contents at the right-side panel. Now, right click on the folder that you want to download and select Get Latest Version from the context menu to download it:

This will download the entire folder from the server to your local workspace. You can then modify any file/folder and check-in to the remote repository.