Backlink Relevancy - Help needed

Greetings Warriors

I'm a beginner (I've spent a great deal of time reading about IM, though I have not taken any real action towards it until now), and in the starting stages of researching the market for a niche that I'm planning to target. After having spent a few weeks crawling WF, I've started researching some keywords, along with my potential competitors currently dominating the top rankings of the niche, trying my hand on some basic reverse engineering in the form of having a look at what backlinks they have. I see that many of these sites have a good number of backlinks from other sites that have very little relevance (if at all) to the niche I'm targeting. Some of these sites have also been in existence for quite a long time. This leads me to the question of this post:

Isn't that a big no-no in the eyes of Google? Aren't these sites risking getting smacked by the Big G? What would in your opinion be a proper and cost/time effective method of link building without getting slapped by Google in the long run, yet at the same time not wasting too much time and money, and would you care to share the steps taken in how you tackle the matter? I see so many various opinions and/or preferred methods and solutions on this topic, and unfortunately lack the experience to tell which one's better from another, and more importantly which one is white hat and which one is black hat...

Any thoughts/tips/advice will greatly appreciated. My thanks for your time, looking forward to see your replies

Alex P