The basics are easy; breathe in, breathe out, repeat...
Here's an app by the marvellous Michael Townsend Williams to help you go a bit deeper... Breathe Sync
The last 12 months I have been taking three or four very deep breaths each day. Normally before going to sleep or after waking up. Breathing in deeply starting to fill the belly, then up to the diaphragm and into the chest and as high up as possible. The lungs as they fill, because they surround the heart, are giving it a massaging embrace, and I found a noticeable lift to my mood after just a few days.
The other thing that has helped me in a general way, is monitoring my breathing to see when I absent-mindedly hold my breath, and actively changing any such habit so that I continue to breath in those moments. The most noticeable was when I was bending down to open a low cupboard or pick something up. So now as I bend, I make sure I keep breathing and of course, remain free in my posture. See the Alexander Technique post for more about posture.
If you try either of these experiments, do let me know what you notice, if anything.