Even though this is a pretty basic SEO question, getting listed in Google (and other search engines such as Yahoo and MSN/Live) varies based on several factors. Here are the most important points.
Links Pointing into Your Website
If there is a link on another website pointing into yours, the search engine spider will follow it from their website to yours. Once the spider follows that link, it will see that your site exists and add it to its database (after all, Google is really one giant searchable database). To get a website or webpage indexed faster, you should make sure that there are several links on other websites or other pages within the same website for Google to find and follow. So, if you have a new page on your website or have changed the content of a given webpage, make sure links are pointing into it!
I have achieved top 10 rankings among millions of results for a competitive keyword term within 24 hours (possibly an Internet record!) after starting from scratch. Admittedly, this is not common for most websites but it can happen. I find that as Google gets more stringent and more competitors arise, it becomes more difficult to get this type of quick result for competitive terms.
The size of your website can have an effect on getting into Google. If you launch a small business website with, say 15 pages, chances are good that if Google can find one page within the site, it will easily find the rest and list all of the pages within your site in a short time. That “short time” can be anywhere from a few days to a few weeks.
If you have a large website with thousands of pages, it could take weeks for Google to visit and process every single page. If you have an established website with thousands of pages, Google’s spiders may take 3 months to re-visit all of the pages on the site. If you have an important change that you want listed, it’s best to get some worthwhile links from other pages and websites.
Another factor is when your hosting was set-up. You can have a domain name registered for years without a website but within a few days of setting up hosting, Google will often visit and index what’s there. In many cases, even using the default page that the hosting company provides (with messages like “Click here for the best hosting” or “This website is hosted by Company ABC”) can get listed. Sometimes these pages actually get into the search engine results pages. I’m not convinced that they are long lasting listings, though.
The Popularity Issue
I’ve had a few experiences where I had written an article which received mild but acceptable traffic for several years. When a story broke on TV that related to the article and I was among the only ones to have written about the now hot topic, there was a gigantic flood of traffic to the article. In those cases, I found that Google was indexing the page in question several times per hour as I adjusted content during the day to bring in even more traffic and capitalize on the media attention. In most cases, this was not due to links coming in from bloggers who found out about the story and linked to the page, or a similar surge of inbound links. This is a very rare occurence for most people but it was very interesting anecdotaly.