The most important thing you are going to need to know is the proper footwork technique and ice axe technique and to go with someone experienced.
Self arrest is something good to know, but is FAR too heavily emphasized, as it takes much practice in order to be effectively used when the time calls. As a beginner, better to learn good climbing technique and how to stay on your feet, than how to fall.
Wear a helmet and if the person you go with has little experience, don't rope up to them. Using a rope effectively relies on having at least one person who knows what there doing.
May and June are probably the best months and definately go mid-week; the weekends at that time of year can be a kook-fest.
And finally, better to go with a guide service than a climbing club, as you will learn better and more up to date technique.