Wifi
ESP3D
See https://github.com/luc-github/ESP3D
For wiring simply use the “Serial” port, see https://github.com/luc-github/ESP3D/wiki/Smoothieboard
Also this project should allow one to use ESP3D with Smoothie's designed-for-Ethernet web interfaces, except now thanks to this they are wifi-compatible too: https://github.com/luc-github/smoothieware-webui-for-ESP3D If you test this and succed or fail, please report either to wolf.arthur@gmail.com so I can work on improving things. Thanks!!!
Ethernet to Wifi
Smoothieboard v1 currently does not have a native Wifi interface.
However, it is possible to easily make it Wifi-capable by connecting it's Ethernet interface to a simple Wifi/Ethernet bridge.
For example, this $15 Wifi/Ethernet bridge will easily make your Smoothieboard Wifi-compatible.
For instructions, see the manual of the bridge you select.
This also generally has the advantage of being much more reliable and efficient than an “on-board” Wifi system which can be found on a few other CNC controller boards.