If you've been looking for a save button on Roadtrippers and can't find one - don't worry, you're not crazy! There is no save button because Roadtrippers saves your trip automatically.
As long as you're signed into your account while working on a trip, the trip and edits will be saved automatically while you're working on it. You can view your saved trips by clicking the profile icon in the top right of Roadtrippers.com to go to your profile page or if you're in the mobile app, tap the Profile option in the bottom menu.