Since you are early in your career, I'd actually advise against pushing too much on specifics of reputation building. That can come later, but you can afford do let it develop naturally.
Instead I'd advise two things. The first is to learn you subject as broadly as you can and to pick one or (preferably) two sub-topics that you are interested in and into which you can delve deeply. This might depend on local resources, of course. Eventually you will need to become the world authority on some (perhaps tiny) area, but getting there depends on knowing a lot of related things.
The second is to find ways to associate yourself with researchers and scholars, whether as a member of a research group (as others here advise) or just finding a mentor or two whom you would like to emulate. Read their papers, ask for ways to delve deeply, etc. See if they will listen to your ideas. Ask them to point you in profitable directions.
But don't neglect your studies.
One way to associate with other professionals is to attend conferences in which the superstars not only present their own work, but are willing to sit around during coffee breaks and discuss ideas in the field. Even if you don't contribute to such discussions, listening will teach you some things, though sometimes they just discuss dogs and pubs (not publications), etc. Even better if you can participate in a conference as a presenter of some kind, even with a poster session.
Learn to swim in a sea of ideas. Get feedback on your own.
Writing is always good. It is especially good to write in a journal in which you date your ideas and get someone else to sign and date your entries. If you have especially good ideas this can establish your priority. Writing for publication is a more difficult skill. It takes practice, and feedback. Reading is just as important, especially for a new comer. You need to know what has been done so that you can build on it.