Hi Rocho @EagerToLearnUX
Welcome to the UX Mastery community!
Design Kit is quite a wonderful resource for learning about different tools. This was put together by IDEO – a widely respected and renowned design consultancy.
The methodology that is described on their website – design thinking – is a relatively new concept (well, compared to other disciplines, design thinking, despite being a few decades old, is still new 
)
Not only is the field new, but is also quite flexible. As a result, several design leaders and consultancies have come up with their own methodologies. IDEO alone has 2 different frameworks for design thinking (Inspire-Ideate-Implement and Hear-Create-Deliver). There is also the Stanford d.school framework, and the Double Diamond model. I am more familiar with the Stanford d.school methodology as opposed to the IDEO version of design thinking. But from what I understand, the basic principles of all these “flavors” of design thinking are pretty much the same.
Regarding your question about which method to use in which phase: The tools used in design thinking are not set-in-stone or attached to a specific phase. Whether you follow a 3-phase, 5-phase, or even a 9-phase design thinking methodology, the tools you use will vary based on your project. Every project is unique and will present its own constraints and peculiarities. Which tool you use in which phase comes down to what you are trying to achieve. For example, you could use prototyping as a method to better understand your users (empathize, gain inspiration). It needn’t always be used for testing ideas.
It is also important to remember that the design thinking process (across all frameworks) is both iterative and non-linear. You could jump from one phase to another – both backward and forward – and even skip a phase, depending on what you learn from your activities.
If it helps, here are some resources on design thinking that might help clarify what I’m trying to convey:
I hope this helps.
Best wishes!
