Firstly google checks your site through a web device called Googlebot, the term for it going through your site is called crawled. Often why Googlebot is refered to as a spider. Once indexed you get a page rank. This is a priority ranking for search queries on keywords. The better the rank the higher you will feature in search results. Anyway getting higher rankings on is down to many things but most importantly for a starter is to have alot of words. Google doesn't take much notice of pictures and java script. So write alot and often. One thing it doesn't like is seeing text duplicated on other sites and it may affect your overal page rank. Therefore don't copy others works. Also try getting backlinks, which are hyper links back to your site from external sites. I will not be going into detail how to do this here but have plenty of information on my blog.
Right so you have a great site some high value backlinks now to get indexed. Honestly you will here loads of alternative methods but the easiest the simpliest and most effective is getting submitted through Webmaster Tools. Its a programme by Google where you submit your site to be indexed. You need to follow the steps as instructed. they are quite easy to follow. After adding your web address you should get asked to verify. Do this now, and choose the meta tag option over the download file. As it instructs on the website paste this into the HTML code in your website/blog. Put it between the two <> tags. Usually i put them right under the first tag but any where is ok as long as your not breaking another tag. now click on verify on google and within seconds it should say verified. Then just wait to get indexed, this may take a few weeks. Remember to submit sitemaps. The best way to do this is to submit your Atom feed to it. To do go to the site maps tab on webmaster tools. Type in /atom.xml at the end of your web address and wait for them to get submitted.
This is the basics of submitting you site for indexing on Google. 1 down 2 to go...... Good luck.