Excuse my buzz word but I think the only way you can make it spread is to embed a virus. One of the things you can do is to enable user to share his search with friends/family over facebook, twitter etc. They could help him adding additional elements to the search (i.e. if they find something on the web that user is looking for they can submit a link), or give other advice.

SEO will not work - as it didn't work for Dropbox. Nobody is waking up one day and start searching for such a tool that you provide.