You're right, link building is important and it's still an important part of Googles' search engine algorithm. What I would do first is go to Moz's Chapter 7: What is Link Building? to make sure you're familiar with the overall strategies and see some examples.
What we generally recommend is starting with looking at your particular niche and the keywords you'd like to rank for. Make a list of your top competitors and start looking at what links they have (you can use Open Site Explorer to find your competitor's links). See what types of links they have and see if you can get similar links (or get linked on the same sites). Focus on getting quality links to your site, not just "easy links".