How to remove the barrel depends on how the gun was made.
Almost all of the old guns have a screw that holds the tang at the rear of the barrel in place. This screw may be a wood screw going into the wood or a machine screw that goes thru the stock and screws into a plate on the trigger.
Many old guns also need the rear screw in the lock plate (opposite the lock) removed. This not only loosens the lock but on many old guns, this screw goes thru a hole located under the tang in the rear of the barrel.
Most old guns use small pins that go thru the forestock wood and engage underlugs on the bottom of the barrel. There are also pins that hold the ramrod thimbles onto the stock. Usually the pins that hold the ramrod thimbles in place do not have to be removed but if you see similar pin holes near the thimbles, those are almost always there to hold the barrel onto the stock.
To remove the pins, use a short metal pin the same size or slightly smaller. Tap the pin with a very small hammer to drift the gun pin out.
It is usually best not to drive the retaining pins out of the wood all the way. Just drive them out far enough to be able to grab the exposed end with a pair of pliers and then use the pliers to pull the pins out the rest of the way.
Some full stock guns might use a screw thru the nose cap or thru the thimbles and nose cap to hold the barrel in place but this seems to be a newly invented way of retaining the barrel. I have never seen an original that did this.
If the gun has barrel bands or straps that go over the top of the barrel, these must be removed to remove the barrel. This is more common on military guns.
Hope this helps.