Hi Debbie, welcome to the Lounge!
You ask a good and difficult question for many fans of vintage watches. VC has a tremendous selection of vintage watches (I'm referring to the variations of dials, cases, lugs, movements, metals, etc. - not the volume). Since VC has such a varied collection, the hardest part about veifying authenticity isn't the outright fake/replica watch, but the "Franken" watch - where all the component parts are authentic VC but were not originally assembled as a complete unit when it left VC's manufactuing.
The people on our Lounge are probably some of the most experienced in understanding vintage VCs and many are willing to help answer any serious questions you have about VC watches (just don't put a scan up and say you recently inherited it from a long-lost uncle and want to know what its market value is)
When looking at any vintage VC, I strongly recommend getting the case and movement serial numbers (which are different) and sending an email to VC's Concierge (available throught the main VC website). The Concierge will send this information to VC's Heritage departement in Geneva and confirm whether the case and movement were originally assembled as one watch as well as information of year of manufacture.
Chances are most vintage VCs will need to be serviced, and though it can be expensive, I think its best to send it into VC for a full-service. They are in the best position to identify anything that may be wrong with the watch and to fix/repair/replace anything in order to get it back to "as new" condition. They will give you an estimate after inspecting the watch, so you can decided then whether its worth the service/restoration cost.
As to reputable dealers, I know of a few that have authentic, vintage, watches - but none of the seem to really know enough about the condition and details of the watch for one to understand the details. They are also fairly expensive. The major auction houses are another option for vintage VCs, but they have additional premiums above the winning bid price which I don't like and their experts don't always catch everything in terms of the watches' conditions. I'm sure if anybody can recommend dealers, our moderator Alex will insist it be done through Private Messaging.
I love VC's vintage watches and am glad to see you have an interest in thems as well. Please feel free to ask any questions, I've learned a tremendous amount over the past couple of years and continue to learn more and more through the kindness and knowledge of our fellow Loungers.
Best Regards, Dan