Assuming the older bottle has been kept appropriately on its side while in your cellar (if not, the cork has probably dried out and the wine is possibly spoiled), take out the bottle and stand it up for about a day (or at least several hours) before you plan to drink it. This will allow the sediment to fall to the bottom of the bottle. Of course, if you’re like me, you decide to pull a great old bottle out of the cellar about thirty minutes before you drink it, no big deal, it’ll just take more patience in the decanting process.
Next, you’ll need a decanter. There are really beautiful, hand-blown Austrian crystal decanters (made by Riedel) that are elegantly and exotically shaped or use an old Beringer carafe, or even a large glass jar it will work just as well. You’ll also need a lit candle, stand-up flashlight, or about any other light source. After uncorking the wine, pour the contents slowly into the decanter, with your light source behind the bottle neck so you can see the sediment---which will hopefully collect in the shoulder of the bottle, just below the neck. As soon as you see the sediment coming to the top of the bottle, you are done pouring the wine---though if you’re careful you can probably get a few last drops in without mixing in the sediment. If you don’t have the patience to decant in that manner, a shortcut is to pour the wine through a coffee filter into the decanter. There are also several neat little filter-type gadgets you can buy to put over the bottle too.