To sneak in Project Zomboid, you will need to press the c key to crouch and avoid going out in the open near zombies. Pressing the c will put your character in a crouch position that is quieter than walking. You can use the crouch button to sneak along walls and lower your visibility as well.
Zombies will also have a higher chance of detecting the player when they reach a certain distance. To avoid getting detected, we recommend keeping a safe distance between you and the zombie you want to avoid.
Along with keeping a safe distance, you will want to avoid making any noise while sneaking. Leveling up lightfoot is an excellent way to avoid making noise, and you can level it up by simply sneaking near zombies.
Sneaking around zombies will also have the bonus of leveling up your sneak skill, which will make it much easier to sneak around the undead.
That said, try sneaking around Zombies if you want to get better at sneaking. If you get caught, don't worry, as you can easily outwalk any zombie that starts following you. But if more than one zombie starts following you, we recommend losing them in buildings or the woods.
For more on Project Zomboid, we at Pro Game Guides have you covered.