1- Submit Your Blog URL to Search Engines!
This is the first and most important step. You have to submit the address or URL of your Blogger blog to search engines. Tell them you're here & ready to rock. Here is a tutorial:
Blogspot SEO: Submit Your Blog to Google, Yahoo and Bing Search Engines
2- Submit Your Blog Sitemap to Google!
After submitting your URL, you should also submit your sitemap to Google. Sitemap contains links to all of your posts so it will help search engines crawl deeply. Google offers a very convenient way to do that through Google Webmaster Tools. Here is a video tutorial to do that:
Blogspot Video Tutorial: Submit Blog Sitemap to Google via Google Webmaster Tools
3- Add a Followers Gadget & Encourage People to Follow You!
Blogger offers a fantastic gadget called Followers. It allows people to follow your blog which means whenever you'll publish a new post, it will appear on your followers' dashboard. For details see these links:
-> How do I add the Following gadget to my blog?
-> What is Following?
4- Get High Quality Inbound Links!
If someone has a blog related to yours then you can request him/her to put a link of your blog. If you are writing original content then ask visitors to link back to your blog. They can simply add your blog link in a post or sidebar gadget. Google loves the original inbound links.
Another good practice is to link to your older posts in the new posts. For example, in the first 2 points of this tutorial, I've linked to my previous tutorials. These are internal links.
5- Search Engines Love Fresh Content!
Make sure to add quality content and write often on your blog. Encourage comments and answer them regularly. Search Engines love updated content and will crawl your blog constantly. Don't copy from other blogs because duplicate content can result in severe punishments by search engines.
Nothing happens overnight. Don't be disappointed if you're not seeing any sudden changes in traffic. Changes can take at least a month or more depending on your blog's popularity and content quality. Install some tracking service (Google Analytics or SiteMeter) to keep an eye on your traffic and monitor the results. Feel free to ask any question or share anything good.