I learned the hard way, I always snowboarded with my friends who raced on skis, so naturally they went on the steepest, fastest trails.
I followed them and I always followed them on like black diamonds, and I'd always get my ass handed to me. This was of course after I learned basic stuff, but I was no where near ready for the type of trails they were bringing me on. I would always be last and they would wait, but they said it was better for me. They joked and said, it builds character!
But it worked I guess. I'm a solid, solid rider now, obviously not perfect, but you get the idea.
I'm not saying go all out, because it's easy to hurt your self as a beginner, but don't judge a trail on it's ratings. I've been down tons of blacks that seemed like greens, even blues at best, and some pretty freaking gnarly blues that surprised me big time.
Ride comfortable, ride within your limits but push your self a little bit more each time and you shouldn't have a problem getting to the point where you can ride almost all trails comfortably.
Also, protip: watch others on the lift.