No, they will not automatically find you. Just drop a few links to some do follow social bookmarks, and you will get indexed.

Go buy a WSO pertaining to pinging

you need to submit on google for index you can ping them via social bookmarking sites or other sources. If you content is good and have user friendly approach then you surly get index fast on google search.

Link building is a very good way for not only getting indexed but getting some good SERP for your targeted keyword. You can drop some useful comments on blogs related to your niche thus gaining backlinks in return.

Social Bookmarking is another good way to get some good high PR backlinks. You can search on google for high PR bookmarking websites.

Article marketing is another good way to get some decent backlinks.

Hope this helps.

"you need to submit on google.........." Whatever you do DO NOT submit on Google!
ViralSO-CEO & akazo gave you some very good advice. One good backlink and some pinging will get you indexed.

Are you referring to just getting indexed in Google or actually getting a high ranking in Google?

[DELETED]

If you want to get indexed quickly for free
http://feedshark.brainbliss.com/
Blog and Ping Tool - Use Pingler.com to Drive Traffic your Blogs and Websites
Blog and ping | Pingoat
https://www.google.com/accounts/ManageAccount?hl=en
Ping.fm / Update all of your social networks at once!
With ping.fm join as many of the sites you can then just post your url and use 140 characters of text (including your url)
The google accounts can give you some high no follow backlinks
This will get you indexed very very very quickly
Create an account at IceRocket Free RSS Builder mash all your rssfeeds into one feed then get someone on fiver to submit this feed for $5 to 70rss agregators (or do it yourself over time)
Cheers
Andrew

Just in case if you want to check that your site is really index or not,

visit this site http://ismysiteindexed.com/

to check whether your site is index or not...