it takes a long time to understand wine. i'm not sure the best way to do it- by starting with milder blends or by deciding on a varietal you like and getting to really know it, then branch out from there.
probably the best way to do it is to stick with one style until you figure it out. the same grape can be influenced by so many factors that you might think you're drinking a completely different varietal. maybe start splitting a bottle a night with your wife. don't spend too much, you won't know what you're tasting and a lot of the more expensive wines aren't meant for immediate consumption.
on the weekends make it a game. decide on a grape, let's say chardonnay. you each buy two bottles of chard, one that is <$10 and one that is between $20-$30. don't tell each other which is which. you each serve each other your wines and jot down some thoughts on each and talk about them while you're drinking them, try to figure them out. after you've knocked down half of all four bottles, which would be a bottle each, make the big reveal to each other. then compare notes and talk more about which you liked and why. it's pretty fun.
i was lucky, i started working at a liquor store around the time i turned 21 and in an effort to get us to sell more wine (because the margins are so high on it), the owner had us take classes and drink it a lot. even though i've been drinking it forever, i still learn a lot.
also buy a decent book about wine and learn about the different grapes and their history.
