Apparently I forgot to include some wifi support in Slax. I don't have any device with wifi here at the moment, so I can't test, but there should be few things to consider. First of all, you will probably need some firmware for your wifi adapter. I'm not sure which packages to install, some of them may not be in official debian repository. Hopefully somebody in the comments will suggest something. Second, you will probably need some software to manage your wifi connections. Some people suggested wpa_supplicant, this can be installed with
apt install wpasupplicant. This is a commandline utility, as far as I can tell. If you are looking for a GUI to configure your wifi network, you may try
apt install network-manager-gnome nm-applet &
Or better (half download, only 50MB):
apt install wicd wicd-gtk -t &
This will put an icon in system tray, which you can use to access network settings using GUI.
Hope this helps a bit.