Changing from a Waterfall mindset to an Agile/Scrum mindset - where do I begin?

I want to start adopting an Agile/Scrum mindset.

That's an innovation mindset in which people learn to build the right thing at the right time. Think of each monthly release as a learning experiment and an opportunity to test an hypothesis.

To be valid, each deliverable must be of usable quality. Otherwise the experiment may fail not because the wrong thing was built, but because it fell over and broke.

I'd say here is a fairly decent starting point - to undersatand the differences between agile (aka lightweight software development) vs waterfall (aka heavyweight software development):
- https://medium.com/blackblot/origins-of-the-agile-manifesto-ee9c53d60bde

If the link would not work then try searching for Origins of the Agile Manifesto by Gabriel Steinhardt

Or another point of view, Agile being known as scientific method or trial & error is around the planet since first apes learned how to put a piece of wood on fire or tested which mushrooms were eadible. 

One of the bigger shifts when moving from a Waterfall mindset to an Agile/Scrum mindset is how decisions are made, rather than simply adopting new processes.

While predictive approaches do not automatically imply hierarchy, Agile explicitly promotes decentralised decision-making and team empowerment. The real challenge is moving away from a PM-driven control model toward shared leadership.

Shared leadership relies on trust, visibility, psychological safety, frequent interaction, and empowerment over hierarchy. In practice, this means fostering open dialogue, reducing behaviours like gossip or shutting ideas down prematurely, and creating an environment where all people feel safe to contribute.

In practice, to get here:

• Respecting team competencies by trusting people to make decisions within their domain, building ownership and autonomy.
• Delegate both responsibility and authority. Expecting ownership while retaining control ("responsibility trap"), leads to dependency and hesitant decision-making in the team.
• Encouraging leadership behaviours by giving teams space to lead, experiment, and learn without constantly waiting for approval, is often one of the hardest adjustments.

The "responsibility trap" is particularly relevant when moving from hierarchical to decentralised decision-making. Look out for:

• Not stepping in unnecessarily.
• Not reclaiming decisions under pressure or when things go wrong.
• Allowing teams to lead within clear boundaries, practically giving them authority over their own work.

It is tempting to take control back when issues arise, but this is where restraint matters. Teams need room to fix problems themselves. The balance is staying involved without removing autonomy.

To answer your question, a good starting point for adopting an Agile mindset is changing how decisions are made, rather than simply introducing Scrum events and artefacts.