This is a great way to promote your web site off- and online. First, let's talk about offline press releases. This refers generally to the print medium which includes newspapers, magazines, trade publications and the like. In deciding where to send your releases, choose a publication that appeals to the same audience as your web site's. If you run a web site about teen life, you may want to try and submit press releases to magazines that cater to teenagers.
Most publications accept press releases for no charge at all.
The key to getting printed is ensuring you have an interesting write-up. This is where you might want to spend some money - hiring a professional copywriter. If you are on a budget, talk to friends and relatives. Someone is bound to know someone who can help you find a copywriter. The other side of the coin is an online press release.