Which are the most effective methods which you use to get your new website indexed in search engines like Google, Bing
The fastest way I know of to get new pages indexed in Google is to get links from social media sites especially from a really active account on Twitter with a lot of followers.
If you want pages to actually stay indexed on Google then you need 2 things, unique content (preferably high value content) and Google PageRank. If the page has enough PageRank it will stay indexed in Google. If the PageRank diminishes past a low threshold then Google will move it to the supplemental index or just deindex it.
If your website doesn't have that many pages on it, then it is easy to keep the pages indexed. Just make sure you spread links around inside your site so that the PageRank gets dispersed well. If your website has thousands of pages on it, then some of those deep inner pages can begin shrinking into the abyss. The way to prevent that from happening is to get fresh links to them or to send them more PageRank.
If I launch a new site and I am in a hurry to get it indexed, I will create sitemaps for it typically using Wordpress SEO plugin from Yoast and then go get some social media links for random pages on the site. That gets it indexed fairly quickly. Google finds the new pages right away and then quickly discovers the sitemaps for the site.
I generally don't waste my time trying to get the sites indexed in Bing or Yahoo. I let that happen naturally. I don't usually get enough traffic from either Yahoo or Bing to waste my time worrying about it much. 90% of search engine traffic typically comes from Google on my sites. There are some exceptions, but that is the general rule. By the time I start building real traffic to a site in Google, the other search engines have already indexed the most important pages on the site.