This is a question I gave to myself 4 years ago when I started leading the Digital Distribution area within my former company. Legacy IT systems, people that have been there for 30 years who don't want to change and a really small budget to play with. No money for coaching, for consulting or anything because the high level management buy-in of "Agile" as a new way of working was not in the top priority list.
My answer to the question at the time was: I will try on my own, in my small circle of influence and see how far I get. Starting a digital transformation process in a corporation with more than 6000 employees and more than 50 years of success doing exactly the same is not a quest for one person, but if you are lucky to be a leader and have a great boss behind you, it is not impossible. The first thing I invested in was my own knowledge and skills: I paid for the best training on Agile and Scrum Certifications, made a Coaching course and started practicing coaching sessions with people I did not know out of office hours.
I did not wait to finish the course to put into practice the theory as soon as I had the chance. My Scrum Alliance trainer said something that I will always remember and has been a key for the success of all the projects I led since then: You can forget everything about Agile and Scrum but don't forget retrospectives. They are a must. If you don't want to continue learning more from me, that is the only thing I would suggest you to master: learn how to lead a retrospective session with your team. It is a powerful tool and if you have the right people, it is also empowering for them and yourself.
After that, I took advantage of my position as Head of Online Distribution to change the way my team understood their roles and their approach to work. We had sessions on vision, sharing our personal values, our personal goals (including leaving the company if that was the case) and receiving feedback from each other. Transparency is a value I was born with and I embed it in any meeting with my direct team of reports. Call it Agile or just a different way of working, those were my keys to building a real team.