It'll take some work, but becoming a Data Scientist is a great career option! The amount of data to be analyzed is only growing as our world becomes more connected, so the demand for data scientists is likely to grow in the coming years.
As for how to get there, it depends on where you're starting from. If you don't have it already, you'll probably want to start with some basic math background: if you can find a basic statistics course at your school or university, or online, that'll give you a good footing upon which to build.
You'll also want to familiarize yourself with at least one programming language. If you're having a hard time choosing, Python is a great choice for Data Science. R is another good choice, though it won't be as generally applicable outside of Data Science.
With an understanding of basic stats, I'd suggest familiarizing yourself with the tools that are available for data science work, and getting into some analysis projects using open data sets that are freely available online.
One of my favorite tools for data science work is the Anaconda Python distribution. You can download it here: https://www.anaconda.com/
Anaconda comes with built-in support for using Jupyter Notebooks, which are a great way to interactively run Python code and visualize the results. Learn more about Jupyter notebooks here: https://jupyter.org/
Once you're familiar with the tools, you can try running through some data science tutorials, and also try analyzing one of the many publicly-available data sets that are online, like the ones in this list here: https://github.com/awesomedata/awesome-public-datasets
Try to build up a portfolio of analysis projects that you're proud of, and publish it online (e.g. via GitHub) so that you can use it to show to prospective employers.
You'll probably want to take some other stats and data-science focused classes too, but don't feel like you need to finish all of the classes you want before digging into some analysis projects on your own - it can be really motivating to have a project that you can apply your newly-found skills to, instead of just thinking about them in the abstract.
The answer may not be as easy as you would think.
Think about what you want from being a data scientist and how you would define success; is it the company you want to work for, the type of work or industry vertical.
What are your aspirations:
--A great statistician who can build custom algorithms?
--A great applied data machine learning engineer who applies day to day problems with existing algorithms?
--A strong visualizer and story teller to the business side?
--A great orchestrator of the process of building, maintaining, and updating ML projects
You usually become successful with what you enjoy or love within the field. But, no doubt, you must have competency, work hard, and show your abilities thru many of the online tools to showcase work: Kaggle, etc. if you do not have direct access thru an employment channel. Google and Amazon are great starting places to get a Cloud account and learn the products and they have free datasets to use.