You can either go online to VFW.org and fill out an application, but this application will not make you a member of your local post. Going to the Post you want to be a part of is the best option.
Walk into a post or visit their website, fill out the application, and bring that in with a copy of your DD-214 that shows that you were deployed and or served during a War Time era. This applies to the waters around that area as well. If you are currently on Active Duty you must bring in orders that show you deployed.
Having a Korean Service Defense Medal will also count if you served in South Korea. If you do not have Korean medal, you would have gotten an Overseas Service Medal, bring in your DD214 and either as award or orders taking you into Korea.