To shoot it you will need some #11 percussion caps, some .451 or .454 diameter lead balls, some black powder or synthetic black powder like Pyrodex or 777, and some form of vegetable based grease like Crisco.
You also should have something to measure the powder and there are many adjustable powder measures available or a metal flask with a changeable measuring/pouring spout. This measure needs to be capable of measuring powder charges of at least 0-45 grains as this is the range of powder loads you will be using.
To load the gun, first put a cap on each empty chambers nipple and "pop" the caps by cocking and "firing" the gun. This cleans out the nipple holes.
Then, with no caps on the nipples, pour a powder charge of 20-30 grains of powder into a chamber.
Place a roundball on the chambers mouth and rotate the cylinder under the loading ram. Use the ram to shove the ball down onto the powder charge.
Load the rest of the chambers using the same process.
After loading the chambers place a dab of the Crisco in each chambers mouth and push it down so it totally seals the area where the ball contacts the chamber. This not only provides lubrication for the balls but it prevents the "chain fire" that can sometimes occur with these guns. (Chain firing is when more than one chamber fires from the flash from the chamber being fired.)
Cap each nipple on the cylinder and your ready to shoot. Make sure each cap is pushed fully on the nipple and it is not loose. If they are loose, pinching the mouth of the nipple a bit with your fingers will deform it causing it to fit tightly on the nipple.
Some shooters use fiber wads between the ball and the chamber to provide lubrication and prevent chain fireing.
After each shot is fired, point the muzzle slightly upward and roll your hand to the right so that the gun is laying somewhat on its side while you cock the gun for the next shot. This helps the cap fragments fall free of the action rather than falling down into the hammer slot.
While your cocking make sure the next chambers percussion cap is still on the nipple. Caps falling off of a nipple can cause chain firing.
The 1860 Colt Army was used extensively in the Civil War. Well over 100,000 of them were made during that time.
The engraved scene on the chamber was Colts way of telling people they had a genuine Colt Pistol. It depicts a Navel battle between the Americans and the Mexicans during the American/Mexican War.
To remove the cylinder, use a non metallic rod against the right side of the pistols wedge. Drive the wedge out with a hammer.
Notice that the wedge doesn't come off of the gun. It is held in place by a screw to prevent its loss.
After the wedge is removed, rotate the cylinder so that the metal between the chambers aligns with the loading ram. Use the ram to "jack" the barrel off of the cylinder pin. With the gun at half cock, the cylinder will come off easily.
By the way, the cylinder pin grooves need to be clean of powder fouling and filled with Crisco or something like it. This not only lubricates the cylinder but it keeps powder fouling from getting into the area.
When reassembling the gun do not drive the wedge in too far. The right end of it should be flush with or protruding just a little bit from the side flat of the barrel. If you drive it in too far, it will force the barrel tight against the cylinder and lock up the action.
Have fun!