Crampon & axe
The two tools that keep you upright on snow and ice.
The basics
Crampons and an axe are the difference between walking on snow and climbing on it. Learn them on a gentle slope before you need them on a steep one.
Technique
flat-foot French technique, heels down front-point German technique, steep ice self-arrest the move you hope you never need self-belay axe in, never out
Practice
Practice self-arrest until it's reflex. The first time you actually need it will be on a slope where getting it wrong matters.