Great to hear about your interest in a career in data science. For sake of simplicity, I'll assume your undergrad and/or masters is in a field that equips you with a solid understanding of data and statistics (e.g. major in math, engineering, statistics, etc.). This would be the firs step.
From there, knowing what type of data scientist you'd like to be would help focus your career prep. There's lots of different types of data scientists working in different industries and departments. So you may be able to help whittle down your options if you're slanting towards a particular industry (e.g. Financial Services, Tech), or department (e.g. marketing, operations).
After you've narrowed down the area of data science that piques your interest, I'd simply encourage you to talk to as many data scientists out there to understand what they do and their career path to their position. A good start is working the grapevine of your undergrad/grad school alumni network.
In general, attributes you'll want to have to help you succeed in a data science career include: - Constant curiosity of the world, and desire to answer questions through mining data - Ability to regularly form a hypothesis which you'll test using data (this ability improves and comes with time and experience) - Ability to gather insights out of large amounts of data
Best of luck, Ken