There are items on the market available to make your life easier when you are out with your dog and need to supply him with fresh water. An adapter to a water bottle is simply a cap that will go over the water bottle with a little ball inside to control the water flow. Think of it as a large hamster water bottle. There are also water bottles with sides that flip out and create miniature water bowls. Your dog should also know how to drink out of a running water fountain. Many city parks may have dog water fountains that are low to the ground and require you to just step on a pedal to get the water flowing. Others will only have fountains for people, and you may need to train your dog to use one.
To teach your dog to drink from a water dispenser, you are going to need to practice. You will need access to different dispensers your dog will use for water. So, if you are taking your dog to a dog park, you may need to introduce him to a water fountain while at the park so anytime he is in this situation he has access to water. This should be fairly easy to train and you can teach puppies as well as adult dogs.
To teach your dog how to drink out of certain water dispensers, you may need those items on hand. Obviously, you can't carry a water fountain with you, so you should go to various places that have water fountains and allow dogs to drink. Whether these are higher people-sized fountains or the lower, ground-level dog fountains, he will still need to know how to drink with running water. Taking water bottles on walks and hikes with you can help teach him how to drink directly from a water bottle or from an adapter on a water bottle. Be prepared with treats, lots of praise, and excitement.