I've been to about 3,500m in the Alps, on a glacier. It really just involved putting one foot in front of the other many times.
I've also done some classic 'mountaineering' routes in N Wales.
Mountaineering is brilliant. The absolute apogee of outdoor sports I think. Getting to the top of a mountain, especially if you needed ropes, is just the best
There's really two kinds of mountaineering. UK style where the mountains are small, so you just have to find a difficult way up; and Alpine style where you sometimes need to get the ropes and gear out just to get up at all. There are however plenty of mountains in the Alps/Rockies/Himalayas etc where you really just walk or scramble up, but the sheer size requires you to take a bivi bag and three days of food. Then there are the ones where you have to take a tent, food AND your climbing gear...