Outside of sparkling wine, I try to decant everything. I know, it's a pain in the ass to clean, and you have to give it some time to breathe, but it's worth it. Properly aerating wine really opens up the complexities, provided that the wine itself is of high quality. No point in decanting $8 bottles of shit. A grand wine truly benefits from oxygen, and you miss a lot of its nuances by pouring straight from the bottle.
I chill the wine for a bit, usually in an ice bucket, or if I don't have ice, I throw it in the freezer for about 15 min. It'll warm a bit, once you pour it out, but I like to start off cold. I don't believe in any rule about how much time you should wait before you drink. Usually, the wine changes for me hourly, and it's fascinating to drink and watch a wine evolve over a meal.
Take some time, try it once. It'll make a huge difference, especially if you're drinking a wine that you've been saving, or a wine that you know has some pedigree. Remember - wine is a film, not a snapshot. Give it some time to evolve, and you'll be richly rewarded.
The vessel on the left foreground is your standard wide-bottom crystal decanter. In the back, the small one is from my Riedel 'O' Series, great for drinking Sauternes or Port. The right is my beloved everyday use decanter I bought from Nice. Bumblebee detail on the side, charming.