To use the snapchat app a form of internet access is needed. This can either be in the form of wifi or your mobile data. If you are connected to an active wifi then snapchat will work even if mobile data is switched off. So yes snapchat will work with wifi.
To access the wifi if using an iphone, go to the settings page followed by 'wifi'. Here a list of all the present wifi networks are listed. If there are currently no wifi networks available to you and you do not have any mobile data, it is possible to take a photo on snapchat and send it, (only for snapchat to tell you the snap could not be sent,) then when an active wifi account is available you can send the snap again.
If any more information how to use snapchat, the snapchat website has a support section that will take you through step by step how to use the app, you can find this here: https://support.snapchat.com/ca/howto