the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
We are clearly commanded by the Prophet (peace be upon him) in the Sunnah to clip our fingernails short. This command is directed to both men and women equally.
In cutting nails, it is required to cut the excessive pieces under which dirt could gather. Therefore, the fingernails should not hang over any part of the finger’s free skin.
It is Sunnah to start with our right hand, since the Prophet (peace be upon him) preferred to start with his right hand in all things, including his manner of grooming. `A’ishah said about her husband the Prophet (peace be upon him): “Allah’s Messenger (peace be upon him) preferred to start with his right side in all matters, in his purification, in combing his hair, and in putting on his shoes.” [Sahîh al-Bukhârî and Sahîh Muslim]
There is no preference, however, for any individual finger over another.
The recommendation to bury fingernail and hair is attributed to some of the Companions of the Prophet (peace be upon him).
Source: Islam Today