Let's begin with, when wearing a dress shirt with jeans, do not wear athletic shoes, no matter their color. If you are not running, do not wear running shoes. Unless you have a severe foot ailment, athletic shoes are for athletic activity, not everyday life. Instead, wear dressy sneakers, desert boots, loafers or more casual dress shoes. I will emphasize this footwear advice with a clip from Crazy Stupid Love below.
Here are a few more no-no's before showing you the right way to wear a dress shirt with jeans. You will notice, that although Jerry has progressed to untucking his shirt, he still doesn't look right. His shirt is just a little too long, but I congratulate him because many men wear dress shirts that are extremely too long versus just a little too long. Like Jerry, you might think wearing a dress shirt with jeans is as easy as untucking and going, but that is not the case. A true dress shirt is too long to be worn with jeans and the dress shirts made to the appropriate length are still too long for shorter men. This means you must hem the dress shirt before pairing it with jeans...
An untucked shirt should end halfway down your back pockets, and the front hem of the shirt should expose some of your jean's zipper, not hide it. I usually tell the tailor to hem the front of my client's shirts about 3/4 down the zipper. Then I have her check to make sure the hems are even. You either want the front and back hems matching or have the back be an inch or so longer. This is to accommodate the shirt riding up as you move around.
Another lesson to learn from Jerry's white dress shirt is its size. It is too long in the sleeves and baggy in the torso. When wearing a shirt untucked, flawed fits are more exposed. Make sure your dress shirt fits nicely to prevent a slovenly look. Too big of shirt and your torso becomes a whirlpool of fabric. If the shirt is too tight, it will get caught on your belly and waist band of the jeans - also a sloppy look.
My last issue with Jerry's shirt is the combination of the stiff fabric with a breast pocket. The inflexibile fabric of a regular dress shirt moves well when tucked into slacks because it is secured, preventing excessive wrinkling and creases. When a stiff dress shirt is untucked it is free to fold and crease all it wants. A pocket makes this catching and creasing more obvious. It also makes your shirt dorky. Best to have no pockets on stiffer untucked dress shirts. They look much better on casual long sleeve button front shirts in softer fabrics.