Always carry a poop scoop, which is a specially designed plastic shovel, or a bag to carry the dog mess to a suitable waste bin. If there isn't a litter bin, take it home and dispose of it there.
Dog owners should not allow their pets to foul at random in public areas. Toilet training at puppy stage helps.
If possible, you should encourage your dog to use your own garden - you can then bag the waste and place it in your wheeled bin or flush it down the toilet.
Do not put dog mess in a brown garden recycling bin.