There are actually a few different methods, and all of these methods can be used by anyone if they forget their toothbrush on a camping trip.
First, he can take a cloth and wrap it around his finger. This makes a ‘brush’ than he can then use, after stealing some toothpaste from Dean. Of course, this cloth needs to be washed daily, and he will make good use of his cup of water.
Another method if he can use if he doesn’t have any toothpaste at all or any other supplies, he can scrape his teeth with his finger. Rinse well!
If out in the woods, like when they’re on their way to Wellwood, is a green twig. The fibers of the twig, after chewing on it for a bit, are gentle and great for scraping. This method can be seen on shows like Survivor.