How To Explore Art
I began getting interested in Art via tumblr.
I think this is an excellent way to find some types of art that you have an interest, and hopefully, a deeper connection, with.
You could begin by searching the site for some pieces you know you like; Da Vinci's Mona Lisa, Monet's Water Lilies. If you find a few blogs that posted those pieces post others that you like, follow them. If you find pieces that have been reblogged, trace the path to the source and you could find blogs posting other pieces which you like.
But I will also stress the importance of exposing yourself to pieces and types of art you may not initially think you like. When I began following blogs, the only art I was interested in was Renaissance Art. But some then posted some Baroque pieces, complex mythological and religious compositions, full of movement and passion
And some occasionally posted some simple compositions. A woman sitting at a table for example; a piece I would not ordinarily have been very interested in; but as I looked closer, I saw she was holding a letter, her face swimming with emotion. I looked at the title: "The Love Letter". For some paintings, ones you initially may have no interest in, or may not appear very complex upon a cursory viewing, the title can clarify and imbue the piece with meaning and emotion. Titles can be incredibly important.
I began following blogs in the belief that the only art I would ever like was Renaissance Art, but I've came out with a greater passion for Baroque, Neoclassical, and Romantic styles of many different subjects, and picked up a healthy attraction to certain french-style pieces, landscapes, and still life, along the way.
Tips
Look up movements
This is a great way to expose yourself to types of art you never knew existed.
Expose yourself to different styles
I never would have thought I'd like some French-style pieces, or the occasional romantic landscape, but some pieces can transcend the style that they are painted in.
Note down any favourite works and Artists
See a work you really connect with, or that completely arrests your gaze? Note it down. Do the same if you look up an artist and find they have a number of works that you really like.
Look up Artists you like
You may find they produced other works that you really like, but if they trained other Artists, you may also like their works, as they will usually be in similar in style and/or content.
Save any works you really like
Either to your computer, or perhaps a platform that lets you easily organise and look up works you save for future reference
Blogs
Here some some tumblr blogs you may find useful as a starting point (they are all ones I follow, and so are mainly classical in nature):
Erotics of Thought - Yours Truly.
Lou Margi - Paintings across a wide variety of styles.
Hildegarda Von - A wide range of paintings, sculpture, and antiquities.
Centuries Past - Various types of Art throughout the ages.
Dido of Carthage - Art, History and the Ancient World
Life Imitates Art Far More - Mainly paintings, but also sculpture, weaponry, and more.
Marmarinos - Sculpture from antiquity
Across Centuries and generations - Various artifacts across a wide range of years
Achasma - Different types of paintings and drawings.
Old Paintings - Self explanatory.
La Clef des Coeurs - More paintings across a variety of styles.
Spoutziki Art - Paintings and occasional art talk
Catharsis - 19th century art, literature, and Pre-Raphaelites
Wonder Warhol - Paintings and art talk.
Painting is Poetry - Paintings.
Arti e Bagagli - Paintings.
Classicist Society - Art, Sculpture, Antiquites, and more.
Irina Norton - Mainly portraits.
Echi Romani - Architecture, Sculpture, and more from locations around the world.
By looking at art online, you can learn a great deal about history, styles, artists, and more, including what you like; but nothing compares with viewing the real thing.
You can see photos of Paolo Veronese's The Wedding Feast at Cana, but you will be unprepared for the vast scale of the original upon seeing it in person. You can wonder at the skill required to paint the intricate marble swirls featured in many paintings by John William Godward, but seeing it in person is even more impressive. You can see how solid marble appears to be made flesh in Bernini's Rape of Persephone, but seeing the sculpture in real life at the Borghese Villa, is quite another experience.