The core-connection breath is different than simple breathing and involves a part of your abdominal muscles called the transverse abdominus, or TA. When we inhale we take a deep breath through the diaphragm, expanding the ribcage in all directions. As we exhale we breathe out through the TA, imagining that you are bringing the hip bones closer together with your exhale breath. At the same time, you want to think about a small amount of pelvic floor engagement. Imagine lifting a blueberry or bean with your pelvic floor (a kegel). You can also imagine that the exhale breath lifts your belly button up to your chest. Perform the breaths lying on your back with knees up.
Jessie Mundell says "exhale on exertion" and Julie Wiebe likes us to think about "blow before you go" - both are useful and important. Exhale on exertion means to exhale during the hard part of the exercise. Using a squat as an example, you would inhale to lower and exhale to stand. Blow before you go means to start the exhale before you begin the movement. Back to our squat example, you would begin the exhale after lowering but before standing back up.
Kegels on their own are not as useful (especially when you simply squeeze the muscles rather than focusing on the lift) and can even increase PFD symptoms - it's the TA breath with a kegel that is beneficial in building a stronger core canister. You do not need to do a kegel with every exercise, just with your core-connection breath, but do be aware of a small amount of pelvic floor lift in challenging movements, and even while coughing, sneezing, or laughing. And exhale through TA on the hard part of every rep of every exercise!
Ideally the core-connection breath should be done daily - you can aim for 10 reps, 3 times per day. I like to pair new habits with things I already do, like brushing my teeth.