See ESP3D on GitHub.
For wiring, simply use the “Serial” port, see Smoothieboard wiring for ESP3D.
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: Smoothieware-webui-for-ESP3D. If you test this and succeed or fail, please report either to wolf.arthur@gmail.com so I can work on improving things. Thanks!!!
Smoothieboard v1 currently does not have a native Wifi interface.
However, it is possible to easily make it Wifi-capable by connecting its Ethernet interface to a simple Wifi/Ethernet bridge.
For example, Cheap 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.