I have a new trigger, a Godox brand X2T and a flash,Yongnuo brand YN685. Both devices work well, but the trigger does not have any effect on the flash. Does anyone have any idea why or how I can connect the trigger to the flash otherwise?
If you're trying to control a Yongnuo YN685 via radio using a Godox X2T transmitter, it won't work. They speak different "languages" that aren't compatible with one another.
You can use a Godox X1R receiver attached to the hot foot of the YN685 flash to receive the signal from the Godox transmitter, or you can get a Yongnuo YN622 compatible transmitter such as the YN622-TX for whatever type of camera you are using.
Yongnuo has several different radio systems that are not fully compatible with one another, so be sure any Yongnuo trigger you get can control a YN685 flash. YN560-TX Pro transmitters can also fully control a YN685 running the latest firmware, but previous versions of the YN560-TX can only control an YN622 system flash (such as the YN685) in manual mode - and only if the YN685 has firmware more recent than about 2015.
Just because the Godox transmitter is 2.4 GHz, and the Yongnuo YN-685 is 2.4 GHz does not mean they can communicate with each other. Bluetooth, wi-fi, baby monitors, garage door openers, and microwave ovens all also operate on 2.4 GHz. They all have different signal protocols.
With flash radio triggering, different brands are not compatible with each other, and within the Yongnuo brand, there are three separate radio systems (560, 622, and RT), which are mostly not compatible with each other (e.g., your YN-685 cannot be used with a Yongnuo YN-E3-RT; and can't do TTL/HSS if used with a YN-560-TX or RF-603 II).
So to use the YN-685 with a Godox X1T transmitter, you'd need to attach a Godox X1R (Canon, Nikon, or Sony) receiver to its foot. Just me, but you might be better off ditching the Yongnuo flash, and getting a Godox speedlight (e.g., the TT685) instead, which has a transceiver built-in that's in the same system as the X1T. The Godox system overall, is more expandable than Yongnuo's, since they support more camera systems (Canon, Nikon, Sony, Fuji, Olympus/Panasonic, and Pentax) and have larger-than-speedlight options in their system. And the radio can be used cross-brand.
I would also advocate possibly spending more on your transmitter, and considering an XPro, Flashpoint R2 Pro II, or X2T transmitter over the older X1T (despite it being the Strobist's recommendation: note that Hobby himself uses an X2T). The X1T has some frustrating issues with its physical UI (particularly the control dial), that have been improved on in the later models.