Got a new site and want to get it indexed fast? Daft question, eh?
The best way I have found is to use a sitemap and tell Google about it with Google Webmaster Tools. In my experience it can take about 2 weeks for Google to re-index a fairly small site with low PR (0-3). Submitting an updated sitemap accelerates the indexing or re-indexing process and you can see updated results within 24 hours in some cases. Larger sites will take longer but still submitting the sitemap makes a significant difference in speed.
I have found that typically the other search engines are less important based on Google Analytics results. For example on my content sites I typically find 80-85% of the search traffic is from Google. Bing also supports sitemaps from it’s webmaster tools. We can always hope Bing will become relevant for traffic!! But let’s face it Google got to the prime position because they had significantly better technology and usefulness than anybody else.
Do get the site working first with good titles, etc and verify the sitemap URLs. If you accelerate the indexing with the sitemap but it’s full of mistakes you’re now indexed with all the mistakes. Mistakes such as missing titles, descriptions or duplicate titles can reduce your page ranking so you wasted that first shot of getting in the index.
Google has an excellent tutorial geared at aiming your site and page construction for good search engine positioning. It’s actually a pretty comprehensive SEO reference. Google SEO tutorial.