A quick way to build backlinks is to join a webmaster related forum and post or respond to posts about link exchanges. Most of the top forums related to running or buying websites have link exchange subforums that will make finding backlinks much easier.
By just posting a thread in a forum you’ll be able to reach a lot more people much quicker than if you were to search through tons of blogs and emailing their publishers about getting backlinks and exchanging links. If you post about what type of blog you’re looking for you’ll be able to get more relevant links to your site and maybe from some good PR link sites as well.
You can also try getting some permanent links from blog posts on other blogs by posting for an exchange. This can help get you some great content related incoming links.
Also another option you have is getting one-way links by doing a “3-way” link exchange. You do this by one of the persons involved in the exchange having two sites related to each other and linking to one site while the other person links to the other site, therefore not having any single blog link to each other but rather to a different blog.
One of the best places I’ve found for good link exchanges is Digital Point Forums. There are more out there, but start here and then search out other ones that you like.