This is a real treat... I can see Van Gogh like this one http://images.metmuseum.org/CRDImages/ep/original/DT1567.jpg in such detail, without having to go to the museum. With my degrading eye sights, this might even be better than going to museum.
Am not someone who can claim to "get" art. Is there some description someplace that will help interpret the work of art - for the one you've linked to, for example?. A background of the context perhaps?
(All IMHO, and sorry if it states things you already know:) I 'get' art, and I'll say that 'getting' art is a misunderstood, over-emphasized concept. Find works that move you, that challenge your perspective. Who cares what everyone else thinks or likes? Find your art. Art is in the eye of the beholder; don't worry too much about the artist's intentions - they lost that control once they put it on paper - what does it mean to you, as it is right there at that moment? Art isn't some secret code that needs decoding; it is what it is, to you. Just to get your mind working on it; here are some questions to ask yourself and tips:
* How does it make you feel? To really grasp art, bring the emotional part of you to bear - it's more far effective than the rational side in this regard. Then try to articulate it (which ties in the rational side). If I can't seem to get traction then I just think 'how do I feel?' - not even how does the object in front of me make me feel, but just 'how am I feeling?' - and often, presto, everything comes into focus.
* Unlike real life, nothing in a work of art is accidental or gratuitous (unless it's intentionally that way!). Why is that red line there? What would a different red look like? A much thicker line? A less opaque one? Rotated 90 degrees? Or, why is it set on a sunny afternoon? What if it was cloudy? Nighttime? Moonlight and stars?
* Often the most powerful question: What are the assumptions behind image in front of you? What didn't they paint (or sculpt, etc.)? If it's a Renior of nudes by a stream, the painting assumes there is beauty in pink flesh, in nature, a relationship between those two things, and it assumes there is no shame in it, no danger, but something positive.
If a work of art makes me uncomfortable, that's a great starting point - what is making me uncomfortable? It's just an object; it can't do me any harm or do anything at all. Often the works that make me most uncomfortable at first - the ones I hate - are the ones that I love the most in the long run. The ones that bore me are the worst.
Reading a book on art history can help you understand a lot of the context behind and specific images in the art (X was a big issue at the time, or image Y represented something in that culture), but IMHO it is much more valuable to read later, to learn something that enhances your burgeoning art appreciation rather than to learn about something you aren't familiar with in the first place. Just find what you love.