Please do not say 'by using one handed weapons', is it calculated by the number of times you swing it or the damage output, does it matter which weapon you are using, i/e, will a dagger get more, less or the same exp as a sword or mace perhaps?

Number of hits and quality of item/base damage. A Dragonbone mace will level it more quickly than a dragonbone sword.

Hitting things
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or a private place

Skill xp gained is indeed based on the base damage of the weapon.

http://www.uesp.net/wiki/Skyrim:Leveling#Level_and_Skill_XP_Formulae

Indeed. A mace in the main hand and a dagger in the off hand will yield the fastest results.

2 maces is better with low stamina. Slow but extremely effective.