the setup is described in this post:
http://bbs.espressif.com/viewtopic.php? ... ridge#p333
(This is not a question about using the ESP as a transparent UART to wifi bridge)
There are probably various levels of functionality here with varying levels of difficulty.
The most straightforward would be a so-called 'HTTP proxy' which proxies the connection between a client and a router
Maybe simpler is just implementing a SOCKS proxy, which is more difficult for the client, but if limiting to a supporting application such a s browser, would work for that use case.
Probably the most faithful solution, but most difficult, is implementing router-like behavior itself, complete with NAT (network address translation) in order to bridge the inner and outer networks.