Excellent question, Patrik.
Also, one without any easy answers. I think the basic idea is to realize that everyone's mind wanders and that this is where both the challenge and the beauty of meditating lies. The usual instruction is that every time you feel that your mind has wandered, to 'gently escort' back to paying attention to your breathing. For me, when I first started meditating and sometimes even today, this meant that over the course of 5 or 10 minutes of meditation, I was probably spending about 30 seconds total focused on my breath. The rest was mind wandering.
However, meditation is a skill that you learn with practice. You'd think that just sitting quietly and focusing on your breath would be something you just 'decide' to do and that's it. Instead, it turns out that daily practice will make it easier and easier for your mind to stay there. So, while the effort to bring your mind back to the breath is active (if gentle and lacking aggression), the improvement is a passive process.
In some ways, the benefits are passive, too. What you get out of it (in my experience and according to others I know) is a really nice sense of calm and centeredness. But, again, this grows slowly and over time. Don't expect miracles and maybe even put more energy into noticing how it DOES affect YOU than in looking for any particular benefits it is supposed to give.
In many areas of the U.S., it is possible to go for a weekend or week long meditation seminar. These can really jump start the process, I'm told, although I haven't tried anything like that. I'm really just an amateur do-it-when-I-feel-like-it meditator, and I bet there are people here with much more experience and insight than me.