Watch for cars. Whenever you're on a road, you should be moving against the vehicles and keep your dog on the side that's furthest away from traffic. Speaking of cars, you also need to be seen. If you're going out at night, you should wear clothing with illuminated or reflective strips. Put a couple strips on you dog's collar as well. Attaching a flashing light is even better. Put a clear one facing forward and a red one pointing backward.
Speaking of safety, it's also a good idea to keep your pet on a leash. It should be a length that's long enough to control the animal and no longer. Leashes can prevent sudden dashes into traffic and allow you to control your dog if another animal darts across your path. Ideally your dog should run beside you. Train it by making a correction whenever the animal moves ahead or falls behind.
You also need to pay attention to other runners. A dog and his owner running side-by-side can take up as much room as two runners, making it a challenge to pass on narrow trails. Be aware of those other runners and move aside if they want to pass.
You need water and so does your pet. Bring along just as much water for your dog as you do for yourself. You'll also need something for them to drink out of. A collapsible camping cup can work well. Don't let them drink out of puddles, ponds, streams or the ocean. You don't know if the water is safe and salt water can make dogs sick.
Remember the poop scooping bags. But don't use plastic grocery bags because then you're surrounding the turd, a material that will compost nicely inside a plastic tomb. The preferable choice is biodegradable bags designed for doggie cleanup. Bring a few of them, just in case your pet decides to take more than one bathroom break along the way.
Follow these simple tips, and you can get fit along with your dog.