First and foremost, running shoes should feel good as soon as you put them on, no break-in period required.
When you walk or run in them, your foot should feel secure and snug with no slipping or sliding at the heel, midfoot or forefoot. The upper should hug your midfoot and create a supportive feel, while the toe box provides plenty of space for your forefoot to move naturally.
If you notice your foot spilling over the side of the midsole, that could be an indicator that you need a wide size shoe. Men’s wide sizing typically comes in 2E and 4E, while women’s are typically size D.
A good rule of thumb (pun intended) to determine that you’re wearing the right size is to keep a thumb’s width of space between the end of your toes and the tip of the shoe.