I had similar problems when installing Debian Jessie (8) and upgrading to Stretch (9). To specify arochester's comment you are interested in Network's position in lspci:
lspci | grep Network
For example, for me it is:
01:00.0 Network controller: Intel Corporation Wireless 7260 (rev 6b)
Intel hardware requires firmware. During fresh install, usually I burn standard Debian iso image on usb pen-drive and provide the firmware (for me from: here) with the same usb stick. Then I follow README :)
I also reacall that firmware-iwlwifi package is required for this manual installation. More insights (power-saving, etc.) you can find here.
I would strongly suggest to give Ubuntu (Live USB) a try. From my experience it is easier to obtain a wifi connection with it (for various wifi cards). It can clarify some potential issues.
Did you use GUI Network Manager? It is a good idea to use command-line interface to establish a connection (if you haven't done it already). It provides better output in case something goes wrong (How to connect to wifi via command line). Personally, I'd recommend wifi-menu command (part of netctl; it works on Arch linux, I'm not sure if it works on Debian too).
Good luck with your problem and have a nice day :)
See also this great answer by Rui F Ribeiro.