Congratulation for creating a blog.
Here is my take -
First of all relax a bit. Truth is - One can not expect quick results with google.
If you want to build links to your site, you need to be persistent. Ask yourself a question, why would people link to your site? You have to have something that will help people out there. Right?
So first, you need content. Your first job is to create content that will help your particular niche. ( May I ask what is your niche? )
Normally, a new blog will never rank quickly. So, for the first 3 to 4 months, you should be focusing only on creating content. Once you have a few articles ready, it's time to build links.
How?
1) Let's start with blog commenting. ( Fact is - It is not as effective as a direct do follow links ) But, if you post the comment in your same niche blogs with an awesome reply, you can get really some referral traffic. )
Don't do this over the top by the way.
2) Next, find the relevant forum to your topic. Join them and take part in the community.
3) Next, you can use guest post methods which will help you to get some really quality backlinks. 9 Only if you post on high authoritative site within your niche. )
4) email people about your content and ask people if they would like to mention it on their blog.
5) Read the 3 links the mentor has mentioned above. ( Don't skip the articles by the way. You will get a lot of Ideas on how to do it.)
let us know your progress.
Good luck for your venture.