The game auto-saves frequently. You’ll know if your game has been saved automatically if see the mongrel logo appear in the lower-right corner of the screen.
You can also manually save anytime by pressing the Options button. However, this doesn’t save your exact location and progress if you’re in the middle of a mission. That’s why it’s important to continue with a mission until you reach the next Checkpoint or finish it completely.
While free-roaming, you can also quick-save by pressing and holding the triangle button while you’re on or near your Bike. You can also quick-save when you're near a bunk in a safe location.