I assumed as much, but only asked on the off chance Grecian-style immortality suited you.
You need to develop a skill or talent that impacts as many people as possible. It doesn't necessarily need to impact them in any specific way, just impact them. Fame comes from being known, not from what you're known for.
That said, I'm sure you've already considered the common methods of achieving fame such as acting, singing, curing pediatric cancer etc and found yourself deterred by a lack of latent talent (not a thing that exists, it's worth mentioning) and a lack of motivation to develop the level of skill necessary -or- decided that the method was otherwise distasteful (type of fame unwanted, not fast enough, too unreliable, etc)..
In that case, I suggest Youtube. The effort required, startup costs, skill needed, difficulty level, and risk are all incredibly low. The potential avenues in are many and varied. The resources available as well as zeitgeist are currently at their peak and are readily accessible. The cost/benefit is phenomenal in every way. The drawbacks are that, depending on your angle, there can be a high level of real work involved (at least at first, until you can outsource), the market is, in general, over saturated, and there is a tendency for momentum to build slowly rather than rapidly at first, but there are ways to compensate for these issues if you know the system and do it right.
Now, if you can draw and animate then forget everything I just said, ignore the rest of this and let me know you can draw because your road to fame could be a fuck lot easier. If not- keep reading.
People used to scoff at Youtube fame, and certain forms of it are transient, which isn't the kind you want, but other types are more enduring, and if you're the type of person who can network (honestly, if you can't -or can't learn how- then you can forget fame.), and who is savvy enough to adapt to match your audience then you can achieve what you're interested in.
The main thing though is that if fame is your ultimate goal then don't buy the lie that you can just film yourself having fun and make it big. If you want to use Youtube to achieve fame (and the buckets of cash that come with it) then you can't afford to dick around and hope to strike oil by just playing video games or filming yourself reacting to things (note, I just mentioned two of the most popular genres of videos on youtube.). Nobody gives a fuck about that- and on Youtube you job is to make them give a fuck about YOU (not necessarily the real you, just some version of yourself that you can consistently project).
You need to go into Youtube looking at it like a business, treating it like a business, and being perfect at looking and acting like you DON'T think of it like a business. Business lesson one: Nobody does anything for free, but if you can get someone to do something for free DO IT. I'm not one of those shmucks, so if you want the actual nuts-and-bolts practical advice on how to become famous then you can hire me as your 'manager' (or call it whatever you want) and I'll make you famous, and don't worry I won't ask for money up front- that would be both laughable and suspicious as fuck.
I only want your assurance you're dead serious about this (I hate wasting time) and a (negotiable of course) cut of your profits once you reach 100,000 Subscribers and on. If you're interested, let me know.