Tasting wine is a bit ritual and a bit science, so to get the maximum effect from your bottle, I'd like to share what has been passed down to me.
The first thing I do with a good red wine is to decant it. It exposes the wine to air and brings out more of the flavors. After a while (or until I can't wait any longer), I pour it into a glass suited for that particular wine (or one that's close enough and washed). There are a ton of different glasses out there, but typically if you're starting out, you can get an all-purpose glass and be fine. If you're looking for a bit more though, typically white wine glasses have a more narrow mouth than a red. Whites need to maintain their temperatures, while reds need air to warm and oxidize for a more robust flavor.
I then put my nose deep into the glass and take in the rich odors that emanate from it (this is the best part of certain wines) and then take a sip and "chew" the wine as if I were enjoying a steak. It really releases the flavors and helps you find the "notes of blackberry" and other weird taste combinations that you may find coming from a grape. After that, I put my glass down and, with my fingers at the base, I swirl the wine glass in a counterclockwise motion to let the air oxidize the wine further.
I then repeat the ritual of smelling and chewing and begin enjoying the different textures, flavors and odors that rush along though all of my senses and just sip the wine. Finding the hints of "cinnamon and plum" will come to you as you experience more and better wines.
Go on a tasting, tour a vineyard, don't be intimidated by the rich history of wine, just embrace it like so many others have. It's just important to realize that wine people are the same type of people that go to art shows. Some are pretentious and pretend to know what they are talking about, some remember every stat from every bottle on the planet, but most are just fun loving people looking to enjoy simple pleasures and sensations with other fun loving people. Enjoy!