Hi, what is it you want to blog about? For fun or business?
Very basically...
To get a site ranked in Google, you have your blog set up - Wordpress or whatever (preferably on your own domain.) Get a site map and tell Google to go and look at it. It's in Google analytics, you put code on your home page and this tells Google that you own the site. They start to crawl the site - they do it every 2 weeks or so. They like to see new content being added regularly. You can use pinging services which tells the search engines to come look at the new content on your site. Then you syndicate your content for backlinks and to tell people about your site - G+, Facebook, Pinterest, Twitter, Linkedin, social media in general (bookmarking sites) and maybe put ads (marketing) - solo ads (if you want to build a list and if you're using it as business you should) banner ads, ezines etc etc. Not telling you to spend money though as advertising is a whole other ballgame and I don't want you coming back saying I told you to spend money and you lost it! You can get eyeballs for free and Facebook is a great place to start as there's 1 Billion people use it so you should be able to find groups in your niche and interested people. Don't spam, create good content on your blog and be social. It's all about building relationships and getting a following. It doesn't happen over night. Good luck.