The wedge has a slight taper on its sides.
The taper starts out narrow on the right side of the pistol and widens as it goes towards the left side.
This taper tightens the barrel towards the cylinder when it is installed.
As the others said, use some sort of non-marring material against the end of the wedge on the right side and use a hammer to drive the wedge out of it's engagement with the arbor pin that the cylinder rotates on.
The wedge does not have to be removed from the barrel. In fact, the small screw's job is to catch on the hooked end of the small flat spring that is in the bottom of the wedge to keep the wedge from falling out after it is loose.
You will probably find that it takes quite a stout blow with the hammer to get the wedge loose.
You will also find that after the wedge is loose, the barrel still acts like it is held onto the gun and it cannot be pulled off with hand pressure.
This is normal.
To remove the barrel, place the hammer at half cock.
Rotate the cylinder until one of the solid areas between the chambers lines up with the loading lever ram.
Release the loading lever and pull down on it.
This will force the ram against the front of the cylinder and it will jack the barrel off of the receiver.
When you reassemble your pistol, push the barrel in place as far as you can using hand pressure.
Then, push the wedge into place until it won't move further.
A few light taps with a small hammer or block of wood is usually all that is needed to get the barrel into its installed position. You do not have to pound the wedge in until the right side of it is sticking out of the side of the barrel.
Most Colt C&B wedges don't stick out.
Note: The small hook on the end of the little flat spring in the barrel wedge IS NOT there to catch on the right side of the barrel when it is installed. It is there to catch the screw head when the wedge is removed.
After you've installed the wedge correctly, it will be much easier to remove the next time you want to take your pistol apart.
Oh. I almost forgot to mention, the lower area of the barrel should be a tight fit with the front of the frame after the wedge is installed.
The cylinder will still be loose and it will move back and forth from front to rear a little bit.
Don't worry about it.
This is normal behavior for a cap & ball pistols cylinder.
Also, if you push the cylinder to the rear you will notice the gap between the front of the cylinder and the rear of the barrel is much larger than a modern revolver would have.
This larger gap is needed to provide some room for the black powder fouling that ends up on the front of the cylinder when the gun fires.
If the gap was as small as a modern smokeless powder revolvers gap, the cylinder would lock up after just a few shots.
