As far as I know, you're basically starting from scratch with each hit as in all traditional web apps. And you'd use all the existing web-type tools to keep track of state like sessions, cookies, etc. I base this on my knowledge of ActiveVFP, Web Services, and Calvin Hsia's paper on the subject:
http://www.calvinhsia.com/papers/AdvancedVFPServers.mhtTables do stay open, however, so once they are opened you don't need to close them unless you're shutting down the app. (Although I think Rick Strahl claimed at one time that tables are opened/closed with every hit in a vfp mtdll, I have not observed this). I would advise you to take a look at ActiveVFP since it is a collection of best practices gathered over several years of dealing with this technology.