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I would like to know the steps Mathematica applies to obtain a result.
I have
Limit[n^Log[2, n]/1.001^n, n -> \[Infinity]]
and Mathematica shows 0 but I want to know how it got that result.
Mathematica can’t do that, it uses algorithms which are very different from what you want to see.
There is a set of functions which will return some information about calculation process for some specific entry, but their outputs are total mess – those are meant as development diagnostic, not as help with homework or preparation for exam.
For some types of problems such as limits, integrals, derivatives etc. you can use Math Assistant on Web, which will describe whole solution process in detail.