How Do I Add Shoutbox To My Website?

I'm not sure, but I think Shoutbox is a communications box placed on your webpage that allows users to make comments.
If that's the item you're referring to, that sounds like a simple cgi script.
You'll have to use what's known as an FTP client to upload the script to your webhost's server. It will need to be placed in your cgi-bin folder . (Scripts usually come with installation instructions. You can also get those instructions from the company you got it from as well)
Hope that helps.
I wish you good luck, and God-speed.

There are a few great shoutbox website. Do a Google search.
Top  5 are like
a) www.sbox.ws www.shoutmix.com www.shout-box.com www.freeshoutbox.net www.myshoutbox.com the one you want, register, create and adjust your design and just copy paste the code to your website.
Hope that helps.
Cheerio