Check out Broadcastify: http://www.broadcastify.com/listen/
Broadcastify allows you to stream audio from your scanner to their server (one feed from your computer to the server) The server replicates the feed on demand so if a huge number of people want to listen in to your scanner, your Internet connection is not affected anymore than if a single user was listening.
IIRC, people who provide scanner feeds qualify for a free membership account. Membership accounts enable you to listen to archives of past transmissions.
If you don't want to use a service like Broadcastify, there is significantly more work for you to make the feed available to the general public (e.g. you need the bandwidth/replication servers, web based audio players (typically HTML5/Flash), etc.