In reply to GoneFishing111:
One approach is to get out into the hills in summer do do a lot of hillwalking and scrambling, moving into winter hillwalking and gaining experience of moving over the same sort of terrain in snowy conditions, before heading to the Alps and attempting easier mountaineering routes out there. Joining a club would help you gain the skills and experience safely, while giving you a ready supply of partners.
The other approach would be through rock climbing; maybe starting indoors with a course at a wall, before heading outside with an experienced partner or with a club. Eventually this will converge with the hillwalking route as you find yourself in the hills to approach technical routes.
With the ultimate goal of climbing alpine routes, I started off with rock climbing. I was in Chamonix in summer - my second alpine season - with another couple of inexperienced partners who were more winter walking people. The difference was quite amusing - they were very happy moving over snow in crampons with confidence, but their ropework and ability to protect things well and efficiently were definitely lacking. On the other hand, I spent most of my time with a healthy paranoia that I was about to stab my trousers with my front points and launch myself over the side of a ridge - but when it came to protection and ropework I definitely had the upper hand. I guess the ultimate goal is to become a well-rounded climber, and for that you'll need to get out regularly both on rock and in the hills.
I was speaking to a guide out there too who reckoned that rock climbing is the key fundamental skill to alpine climbing. I wasn't sure I agreed while teetering along a precipitous snow ridge, but in hindsight I'd hazard a guess that crampon and axe skills are a lot easier for a climber to pick up than ropework for a non-climber.
