How do I go about putting a staircase into a loft?
With a high ceiling.
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First, brush up on your local Building codes and pull your permit.
https://extremehowto.com/how-to-build-stairs/
https://m.wikihow.com/Build-Stairs
https://youtu.be/iALK0-n-81c
https://www.popularmechanics.com/home/how-to-plans/how-to/a2145/4224738/
If you wish to avoid the severely inclined appearance, can you build stairs with landings that then change direction? Although I've seen spiral staircases to upper floors, I would advise against it, for safety reasons.