One of my lifelong goals is to one day ascend a dangerous/difficult mountain. I want to be able to look out onto the great horizon and see nothing but clouds and the wilderness below.

Obviously, this is something that people train for their entire lives, and end up having one or two shots to actually do it. My question, is what requirements are truly necessary to attempt it? Being /fit/ is a must, but do the guides/locals permit or allow you to attempt it without having a resume of hikes under your belt? If not, where should I start? I've dayhiked since I was a kid, the longest I've ever spent /out/ hiking was two weeks, which was difficult, however it wasn't under extreme conditions (ascending a mountain at 5,000+ ft). So if you wanted to attempt Rainier, or K2, where would you start?