Linked is a thread from another hiking site, started by a poster who wanted simple, rudimentary, "not overthinking this" information on use of an ice axe. The helpful responses (to his specific questions) start with post 18:
http://www.vftt.org/forums/showthread.p ... On-Ice-Axe
And a useful perspective:
...it is FAR more desirable to not fall than it is to arrest once you have fallen. So focus on not falling. There's an analogy with avalanche safety: some folks get overly focused on what they'll do if they get caught in an avalanche, when the reality is getting caught in an avalanche is very, very bad; one should do whatever they can to prevent that from happening. Same with ice axes and crampons, if you've fallen you're immediately in a very bad situation. Better to not find yourself there. So hone your crampon technique and focus on not falling. (With the corollary that your survival chances are somewhat better if you have decent self-arrest technique if you do fall).
As hiking continues its slow evolution, from multi-week backpacking to ultralight 24-hour traverses, from summer-only to three-season to winter grids, basic techniques are likely to become more commonly needed and implemented. The means to handle snow and ice are a very nice addition to one's quiver.