When you're taught art appreciation, you're taught how to view art. Yes, there is a method, that will enhance your art loving experience. And much of that has to do with taking your time.
I once heard someone complain that art galleries and museums were cold, austere places that were devoid of life and entertainment, giant mausoleums were the art was "hanged" instead of enjoyed.
Clearly this person was unaware of why.
Art is supposed to be the experience. When viewing an artwork, you don't want other things to influence your experience of the work. Not sound, not music, not distraction.... good, great art, will speak for itself without the need of a stimulating environment. Mediocre, poor art, well, yeah... That's going to need all the help it can get.
My first visit to a real art gallery was when I was 12 - the National Art Gallery in Canberra, our nation's capital. It was intimidating to say the least - vast walls with enormous paintings, and everywhere, hushed voices talking, as people wandered through the caverns of human vision. We were with my uncle and aunt, and one of my cousins, a man well versed in art, and an artist himself. As we walked through the exhibitions, he saw that I was confused by what I saw, and began explaining the work to me.
That was the day I decided that I was going to grow up to be a real artist. 
But back to the experience - we're talking about the difference in perception of people who expect, and people who discover. Here I was, a child, in awe of every thing that lived on those gallery walls, and to me, it was a sacred thing, a holy thing, a temple of thought and emotion and vision and inspiration. A temple of humanity.
I had no idea what to expect. I had no clue what I would find around the corner, or what it would mean. And that was the whole point. Each work was another world, and with my wonderful cousin as my tour guide, I was on a journey of discovery that outdid Indiana Jones. And there were fewer booby traps.
When people say that libraries and museums and galleries are boring, that they need livening up, that they need to be progressive and move with the times, I can only think that the time of real study, real scholarship and real art is passing. The need to interfere with such pursuits of discovery of knowledge, the journey of thought and the transportation of vision.... it's not progress. It's a need to fill a void for people with small attention spans, with no patience, and underwhelming imagination.
Enter the virtual gallery.
Here, you can view art as fast as you can scroll, with your tunes playing, and your massage chair switched on, while your incense burns and your puppies frolick on the couch. Here, you can have every intended sensation that you desire, competing with the "love of art" you profess to, while intermittently texting your friends, catching up on work emails, and watching snippets of the latest Russel Brand interview. Yeah. You got it covered. You get to be modern, hip, knowledgeable, productive, alternative, animal-loving and cultured simulatneously.
Don't get me wrong, when life is short, you cram in as much as is humanly possible, and then wish you had a few radioactive spiders around.
Yet it is this very development in lifestyle that is now claiming the development of art.
Which leads me to *insert music cue here* the method of art appreciation.
Choose your artwork. Now put it in front of you, stand back and stop. I mean, really stop. Stop thinking about your grocery list and your mother-in-law, and your latest romantic squeeze, just stop.
Rest your eyes on the artwork. You're not staring, you're resting your eyes in that direction. Allow your eyes to wander, and rest wherever you are compelled to look. Look at the entire work.
Now, if the work is good, it will take about two minutes for you to leave this world behind and become absorbed in the art. If the work is a masterpiece, you will become transfixed. If the work is not doing that, it isn't a bad piece of work, it just wasn't created for you, and move to the next one.
This is possible to do even on the net, but you have to be willing to be patient for long enough for the work to grab you. Much of art these days is concentrating on grabbing your attention, a "wow" factor that hits immediately. The trouble is, much of that kind of work doesn't keep your attention. it's designed for fast impact, not deep communion. Once you've seen it, there's nothing more to it. Great art is something you return to, again and again. Great art is remembered because it does more than decorate.
And I've met people who have been confused by that concept- until I show them the difference. Now, when they look at art, their appreciation is that much deeper, they are far more discerning in their tastes, but more than that - it's not just that they know what they like, but they know why.