The process of decanting wine is actually quite simple. You simply want to take the bottle and pour it slowly into the decanter, possibly tilting the decanter depending on its shape so that it rolls down the side and doesn't splash off the bottom. You may also want to use a funnel and screen to make the process even easier as well as to catch the sediment that may come out of the bottle. That is one of the main purposes of decanting, to separate the sediment from the wine. Older wines will have sediment from the lees (result of the fermentation process) and being left with a mouthful of sediment is not the most pleasant experience. This is why you will see servers decant a bottle of wine over a candle, so they can see the sediment remain in the bottle as to not transfer into the decanter.
The other reason for decanting wine is to aerate, or allow oxygen, to get to the wine at a quicker rate and at a higher volume. Oxygen elicits many aromas and flavors that may be hidden in the wine and take some time to show themselves. The quicker the air is allowed to coexist with the wine, the faster the wine will open up to it maximum potential at this point in its life. Since wine is ever evolving it may smell and taste differently now then it will in years to come. But the decanting process will ensure you are enjoying all of the components that were meant to be enjoyed by the producing winery.