The answer is going to depend a lot on your motivation. Do you just want fame for the sake of fame, or do you want recognition for something that you have or that you've done?

Fame as a concept isn't necessarily complicated, it simply means people find you interesting enough to want to pay attention to you. However there's a huge variety of reasons that that may be the case; people might like your work, what you say, your public persona, etc. There's no one way to get there.

On the internet, it's very possible to play the social media "game" to gather a following. Essentially just being highly active and engaged will do it, though it helps a lot if you're saying things that people agree with, and it helps even more if you present a lifestyle that people aspire to. You can get very cynical here, though in fairness, people tend to respond better to what they perceive to be authentic too.

I would say luck is generally the biggest factor to any kind of success. You don't necessarily have to work hard to be lucky, but hard work will make you much more likely to be in the right place at the right time, which at the end of the day is what it's all about.