The feeds are available only for non-commercial use. This means that you can not display the news feeds on a business's, organization's website or a website which is meant to advertise a business, but you can freely use it on your personal blog. Also, at the moment Google does not provide commercial licenses for the news feeds.

You may use the news feeds on your internal, private network even if you're a commercial entity.

The easiest way to get Google News' content on your website is NewsShow which also has an easy-to-use wizard for your convenience. If you're a bit more than novice web programmer, you may also fetch the feeds using server side code or even AJAX.