If your dog has a collar, you could also hook the leash to both rings (harness and collar) for a more secure fit.
Using a harness for your dog instead of a collar can be a beneficial change for his well being as well as his behavior since it reduces unnecessary stress on the neck and allows him to walk naturally and stress-free, if adjusted correctly. Harnesses are used for different reasons: for behavioral purposes, for safety, for guiding or for pulling gear. Regardless of its function, adjusting a harness is a simple task, yet it is important to take the time to do it well to ensure your dog's safety and comfort.
Make sure the harness is on the correct side before placing over your dog's head. Generally if the harness has a label, it should be on the outside. This indicates the correct way. Also, the front ring for the leash should be on the front.
Place the front loop of the harness over your dog's head. The strap loop might need to be hooked by the buckles for certain harnesses. If so, hook it to its respective buckle and then place it over you dog's head. If placed correctly, one side of the strap should be on your dog's back, behind the neck, and the other part on the front, against his chest above his leg muscle, to allow movement. The ring for the leash should be on the front.
Place and adjust the straps as necessary for this part of the harness to sit comfortably over your dog's chest and back.
Slide the belly strap underneath your dog, without buckling up yet. See if it will be too loose or too tight when attempting to buckle it up on the other side of the harness. Adjust the top and bottom straps by pulling and sliding through the adjusters as you see necessary, until it fits your dog's torso comfortably.
Adjust the front part of the strap (on his chest) one last time, now that the other parts have been adjusted. Make sure your dog is able to sit and lie down comfortably with the adjustments. Make sure his movement is not restricted.
Make sure you are able to put your fingers under any part of the strap, between the harness and your dog's body. If it is so snug you cannot fit your fingers under, it is too tight and needs to be loosened.