The Medium’s chief antagonist, The Maw, is a foe that you cannot fight off in the real world. Marianne has abilities to deal with this grotesque creature in the spirit realm, but you will have no combat-focused defense mechanism against it when it stalks you in the living realm.
Your best bet to avoid The Maw is to remain silent. It is blind in the real world, but it can hear you. Its hearing is so sensitive that it can pick up the sound of your breathing, so holding your breath when it is close by could be the difference between life and death.
To hold your breath in The Medium, push and hold down the right thumbstick on your Xbox controller. Marianne will cover her mouth, so you know that it is working. It does not appear that there is a limit to how long Marianne can hold her breath either, so don’t worry about holding it for too long or thinking that she will pass out from not breathing properly. However, if you do get concerned, release the right thumbstick for a second or two and reapply pressure again.
You can walk or sneak around while you hold your breath, but The Maw can pick up on the sound of your footsteps, especially if you are walking. It is best to remain still and crouched behind cover until it wanders off to search for you in another location. You can sneak around it and escape once the coast is clear.