Once a website has been crawled by google, if it has good content, fresh content gets indexed immediately.
If it's web2.0 or new sites, that is very difficult. But put it this way: To be indexed Google must visit the link first, and if it's a new property (new web2.0, new site, article submission etc) there are two ways for Google to crawl it. One is naturally, and that might take weeks, the other one is linking to the page from an established domain, google will follow the link and cawl the page. (Blog comments do not get followed by Google, but if it's important for you, send a link from some other property and make sure content is decent enough to get indexed)