Out and down.

Draw a deep nose breath to inflate your belly, then inflate your obliques and lower back with a sharp mouth gasp. Flex all of your core muscles outward and downward to create a rigid trunk. Through which the movement generated by your legs will transfer entirely into the bar.
Inflate + flex
Instead of breathing into your chest, take air into your belly, inflating it like a basketball. This will stabilize your entire midsection. To belly breathe, take a deep breath while forcefully pushing your belly out. This should help you use your diaphragm to draw air into your belly. During the lift, try to exhale forcefully against your closed throat. This action, called the Valsalva maneuver will help you build up enough pressure to stabilize yourself under big weights.
When you inhale, your stomach should inflate to the front and sides (which has been described as “360 degree expansion” by Chad Smith and “inflate your obliques” by Chris Duffin), rather than your chest and shoulders rising.
Stronger By Science
When we take a deep breath of air, and our shoulders rise upward, we are actually causing our stomach to sink inward like a thin tree. We want to do the opposite and make a thick tree. I ask people to mimic how they feel, with their stomach, after they eat a ton of food on Thanksgiving. They usually push their belly out, distending it. This pushing out motion creates a “large trunk” like a thick tree. So we first need to take a large breath WHILE we pull that air into our lungs by making the sides of our stomach pull outward, like our thick tree. We then can push outward—focusing on the sides of our stomach—like a pufferfish to initiate our brace and hold it.
Get air into your midsection by focusing on breathing into your low back, this will create 360 degrees of pressure, improving performance and helping your back stay healthy. Get air before you bring the bar out of the rack with your hips.
You want to breathe into your belly ... as much into your belly as you can. If you wear a belt, you try to push into the belt 360. If not you just make sure the whole torso is tight. Typically you can get more air into the torso if you breathe through your nose first into the torso and then your mouth.
This part can be tricky. Once you’re underneath the bar, you’re going to take a big breath in, but you’re going to do that while keeping your core in the same position. In other words, don’t take a big breath in and let the lower ribs flare and the pelvis tilt forward.
Robertson Training Systems
If I'm gonna have you stand in a squat stance and I had a broomstick right and will whack you in the stomach, how are you gonna tense your stomach? How are you gonna keep it tight? Now what if I'm gonna hit you in the oblique? What if I'm going to hit you in the lower back? What are you going to do to be able to make sure when I swing that broomstick the broomstick's gonna break - you're not gonna break. Are you gonna pull air into your stomach? Are you gonna flex your stomach? I'm gonna use a bat, now what are you gonna do? It's gonna be even tighter.
A good way to brace for [low rep] squats is to make sure you take a huge breath, tighten your whole core, make sure your core is [neutral]... that much bracing takes a lot of energy. [For high rep sets] all you want to do is make sure you breathe in, tighten your abdominal muscles to some extent at least and stay nice and upright, focusing on keeping your core tight to make sure it's not wobbly...
Renaissance Periodization
[If] that bar comes up when you breathe, then... it's going to come back down when you're squatting up and... because that comes down, it pitches you forward. So we want to keep [the breath] down.
One really common mistake that we'll see in breathing is people who fail to take the air into the abs and push out through the obliques... Stability is going to be generated here through the obliques, the abs, [and] the hips... So it's air in through the nose, finish through the mouth, push that air down and out through the obliques trying to make your waist as wide as possible.
If you brace wrong or you don't brace at all, it ends up making your core your limiting factor. Not allowing your legs to express their strength as much, not taxing the quadriceps and other leg muscles as much... and that prevents you from getting the most out of the exercise.
Renaissance Periodization