When I didn't pack my toothbrush for a road trip one time I brushed my teeth using a piece of a paper towel.
I got the paper towel a little wet and then put a little toothpaste on the paper towel and then wrapped the paper towel around my finger and then brushed my teeth that way.
If you don't have any paper towels you can also use a washcloth the same way to brush your teeth when you don't have a toothbrush.