Everything seems to work fine except the sound. Do I need to install the correct sound driver for my card? I'm using Windows but I doubt a Windows sound driver can be installed in Tails. How can I fix this?
No, a Windows driver will not work on Tails.
As Tails is based on Debian GNU/Linux, you will need to download a driver coded for Debian. Identify which sound card you have in your machine, the Vendor and Model, and search for the relevant driver.
You don't specify which sound card you have in your question, so unfortunately I can't recommend a specific driver, nor provide the link.
However, some drivers will accommodate multiple sound cards, as multiple vendors will use the same chipset. Most cards are SoundBlaster compatible these days, so downloading and installing a SoundBlaster compatible driver is a good point to start from.
You may find the Debian page, SoundConfiguration, useful.
As Ubunutu is also Debian based, an Ubuntu driver should also work.
It may be just that you have to choose which output to use to hear the sound on your running Tails.
Try to right-click on the sound-button in the top right corner and choose Sound Preferences. Try to choose different options (if you will see more) in the Output section.
Even if this won't work out, you can use this method to write us more information about your soundcard.
I found a solution.
In "Application\System Tools\Preferences\System Settings\" one can click on "Sound" to access a list of sound devices. "Testing Speakers" doesn't work which may give the illusion that none of the sound devices works. In my case I went to YouTube and clicked on a video. Then I went through the devices until I got sound. The "Built-in Audio Analog Stereo" device works for my sound device on my motherboard. :-]