Greetings. The official website is: CMOHS.org - Official Website of the Congressional Medal of Honor Society
The main points are that the award was originally created as a Congressional Bill during the Civil War primarily for the Navy and Marines. A similar Bill was then introduced for the Army and subsequently all Armed Services members were eligible though the history of the MOH includes slight variations for some Forces as opposed to others. The MOH is presented to the recipient by the POTUS in the name of the US Congress: The awarding and due diligence is done by the Armed Services but the award is officially the Congressional Medal of Honor.
The MOH has two significant historical markers/evolutions: 1) The Medal of Honor Legion in 1916/1917 cleansed the Award of less than meritorious recipients which greatly enhanced the MOH for valid recipients before and after that event as it became an extremely rare award, and 2) The MOH has slowly evolved to the point today where a recipient basically has to die in battle to be awarded one.
It is unofficially an expected tradition that senior officers up to the Commander of the Joint Chiefs of Staff and the POTUS must salute any and all recipients of the MOH. President Obama created a tad bit more than a shock by being the first President to ever not show for the MOH Inaugural Ball in Jan 2009.