You see your dog swallow part of a mushroom growing by the path. Contact your veterinarian or an animal poison service immediately, even if the dog seems normal. Some wild mushrooms are toxic, and lookalikes can be hard to distinguish. Do not guess from a photo search, wait for symptoms, or induce vomiting unless a professional tells you to.
If safe, photograph the mushroom and surrounding patch, including its top and underside. Collect a sample in a separate container without risking another exposure and ask the clinic how to bring it. Tell them when the dog ate it, how much, and any symptoms. Vomiting, diarrhea, weakness, tremors, or changes in behavior need urgent veterinary care. Keep your dog away from the patch while you seek help.
Prevent a repeat
For later walks, avoid paths with fungi and supervise your dog on a secure lead. Scan ahead and move away before they can investigate. Practice "leave it" using safe items indoors and reward turning back to you, do not use unknown fungi as a training challenge. If your dog repeatedly eats non-food items outdoors, tell your veterinarian and seek a qualified trainer's help with management. A properly fitted, gradually introduced basket muzzle may be useful for some scavengers, but it is not a reason to keep walking through known hazards.
This is a medical question before it is a training question. Make the call first.
Sources: Dogs Trust: Tips for keeping your dog safe this autumn. VCA Animal Hospitals: What to do if your pet eats something toxic.