I want to try paper embossing at home but have no clue how to start with it.
I don't guess "without any tool". you'll gonna need something to apply weight or pressure on paper, you nails, fingers, a rod, etc. whatever that doesn't scratch or leave much undesired artifacts. If your paper is heavy weight similar to cardboard the results would be better.
first try slowly with thin but dull object like rounded tips of a hair clip, a ballpoint pen which doesn't write, a pen cap on a spare sheet same as your paper. the support you use also should be relatively smooth and not leaving visible/dirt/ink marks on the surface, a couple of normal white papers on a desk would be fine. Start slowly trace the pattern, then move to a larger tool like back of the pen for filling in the shapes. If you were satisfied proceed with your actual piece.
Weight. Like a flower press. You could put the paper you want to emboss between books with the motif or design touching the paper. You could use wood to protect the books.