I am no expert on this topic but few things I do to get my blog Google indexed when I start one and I am almost always successful.
1.
Preferably use your own domain to start a blog.
Write 5-6 original articles.
Carefully choose keywords or tags.
If you are using WordPress, some of the good SEO plugins are all in one SEO plugin, headspace, platinum SEO, greg's high performance SEO etc.
2.
Use pretty permalinks.
If you are using WordPress, go to admin->settings->permalinks->select custom structure- put /%category%/%postname%/ in the blank field.
You need unrestricted.
htaccess file for this.
So your web host must support this.
3.
Now go to admin ->settings->privacy->blog visibility and make sure you have selected "I would like my blog to be visible to everyone, including search engines (like Google, Bing, Technorati) and archivers".
4.
Use pinging services like pingoat.
com or feedping.
com or feedburner pingshot.
You can also go to admin->settings ->writing->update services and copy and paste the urls of pinging services and save changes.
Pinging services alert other blogs and blog search sites that you have posted a new article.
You will find web spiders swarming at your site after posting a new article.
5.
Now go to some other blogs which have articles on the similar topics and comment there.
Leave your website address there.
Don't make your comment look like spam and always put your name in the name field and not something else which can make your comment look like spam.
This is the most important part as Google spiders will eventually come to your site following the links.
6.
Now go to Google webmasters site.
Login with your Google account.
Add your site.
Do the verification as explained there and add your sitemap location.
If you haven't already created a sitemap, use Google xml sitemap generator plugin.
To add sitemap go to Google webmaster tools->select your website address from the domains list->site configuration->sitemaps->click on submit a sitemap.
7.
You can also increase googlebot traffic on your site so that your site gets indexed quickly.
Simply go to Google webmaster tools->select your website address from the domains list->site configuration->settings->crawl rate->set custom crawl rate.
It generally takes up to six weeks to get your site indexed but if you follow above steps, Google will index your site lot sooner and if you are lucky like me it'll be only few days.
WordPress Google SEO can make your blog rock.