Use some free pinging tools online and try to get good quality of backlinks to your site. Then most search engines will crawl your site fast and automatically.
A good natural way to do it is to write an article relevant to your site (i.e. if it's a blog about dogs, maybe write an article about different styles of dog bowls), and submit it to an online article database with a link back to your site. (EzineArticles is a good choice, as Google's bots check it frequently.)