Get into Ultimate Mountaineering
Climbing extremely high mountains or mountains that require a lot of technical skill will probably require you to have a lot of experience climbing smaller/easier mountains first. However, that does not have to be the case, there are a number of tour operators or guide organisations that do allow inexperienced participants. These tours are usually well organised and arrange everything for you (but please watch out for dodgy companies; - there are a few out there) and will advise you on any relevant training, what equipment to bring, and give you loads of information about what to expect on the trip. These organised mountaineering trips do not come cheap though and generally the more organisation the company does then the more expensive the trip will be.
If you have enough experience or are going as part of an experienced group, it is possible to organise and undertake your own trip. This will require a lot of preparation and research as a lot of the really exciting mountains to climb are in remote areas that can be challenging to reach, even before you start the climb.