Inspect the bore. See if the rifling is sharp and crisp. Most old barrels will be fairly pitted.
If it's a new barrel made to look old on the outside, and still be a shooter, then the bore will be nice.
The barrel can be pulled from the stock, and inspect how its fastened to the barrel. Look at the plug that goes in the end of the barrel, there are distinct differences between new and old, with wear patterns, wrench marks, soft edges, etc. that often present on old plugs.
In the end, if it's really well faked, it may be impossible to tell. But it's got to be worth the effort to do so, and few people know how to do that very well, and those that do, will charge a lot for their work.
I'm rambling, but you get the gist. It helps to have viewed a lot of original work. If you don't have this experience, take it to someone you trust.