If you wish to use the normal means of refilling Copic markers, you can use the "drip" technique. Cover the work surface with a protective barrier. Anything from newsprint to a paper towel will work. Open the dropper of a bottle of replacement ink and hold it directly over the dry nib of a Copic marker. Carefully drip one drop of ink at a time onto the dry nib until it becomes recharged. Adding 30 to 40 drops will refill the nib for a limited time. This method works, but won't last as long as refilling the barrel.
You can refill a larger amount of ink in less time by removing the tip or nib of the marker. Put down a protective barrier on your work surface and gently pull the nib from the tip of the marker. You may choose to use a pliers if you do not wish to get ink on your hands. Once you have removed the nib, keep the marker upright, remove the cap from the refill bottle and insert the nozzle directly into the barrel of the marker. Squeeze the refill bottle until you have filled the marker. Replace the nib and caps on the marker and refill when finished.
You may wish to use a similar method to the drip style of refilling Copic markers called the "German" method. Place a protective barrier over your workspace. Remove the caps from both ends of a Copic marker and hold the marker so the small end points down toward your workspace. Open the nozzle of your refill bottle and squeeze the bottle until it drips onto the nib of the marker pointing upward. Continue to drip one drop at a time until ink starts to drip out of the opposite end of the marker. Stop refilling and replace the caps on the marker and refill bottle.
One of the methods recommended by the Copic company involves the use of their proprietary refill "booster." Essentially a syringe needle, the booster allows for easier refill of the markers. You may use it by removing the cap from your refill bottle and attaching the booster in its place. Use caution when handling the sharp tip of the booster. Cover your workspace with a protective barrier and remove the nib from your marker. Insert the tip of the booster into the open end of the marker and squeeze the refill bottle until you have refilled the marker with the desired amount. Remove the booster from the marker and refill top, replace the marker nib and the cap on the refill bottle and marker.