The groom selects his Best Man. It is typically his brother, father, a close relative or friend. In the case of a second marriage, he can even choose his son to be his Best Man.
The Best Man plays an important role. He is responsible for:
Getting the groom to the church
Holding onto the rings
Giving the first toast to the bride and groom
Now, if you read the etiquette books, the best man has a long list of responsibilities, such as... 
Arrange for ushers to be fitted for tuxes
Coordinate ushers' activities on the wedding day
Help the groom get dressed
Stay with the groom up until the time of the ceremony and offer moral support
Make sure the groom is packed "appropriately" for his honeymoon
Make and/or confirm the couple's honeymoon arrangements
Drive the groom to the ceremony
Hold on to the marriage license and wedding rings
Pay the Officiant and other vendors
Give the first toast to the bride and groom at the reception
Oversee the timetable to make sure everything runs on time
Drive the couple to their hotel or their destination after the reception
The best man's responsibilities depend largely on who the best man is and how much responsibility and other tasks YOU would like him to perform.