The best low/no cost method of promoting a website or blog IMO is social media promoting. You can get a real good amount of traffic and website visitors by using a consistent social media marketing campaign on the social networks that best fit your particular niche and needs.
You can use a free or paid service to help automate the process so that it takes a lot less time to do or you can also buy software that can do this for you as well.
The key is consistency and doing it across multiple social media platforms regularly. It's also best to not over-do it as that can be seen as spam by the social sites and their users as well. Just be consistent and try to intrigue the viewers into wanting to visit your website.
You can also promote some kind of give-away of an eBook or something on the social media sites to try to draw people to your site to get the free promotion.
There are many ways but few are going to have the impact right away like social media promoting can have.
