Who wins a Spades trick
Pyth, 28 27 25 bytes

J"KTAZ"hxcz)eo_XN+@z1JJcz


Try it online: Demonstration or Test Suite (first 4 chars are the test suite construct)

Thanks to @isaacg for a trick, which saved 2 chars. 

The main idea is to modify chars of each hand such a in way, that the winning hand has the maximal value. 

The values of the hands 23456789TJQKA is already nearly sorted. I just have to replace T with A, K with T and A with Z, resulting with 23456789AJQSZ. 

The order of suits CDHSare for the most not really important. S, the most powerful suit, which is already the maximal value. Important is to give the suit of the first hand the second most powerful value. So I translate this suit into K. 

All hands also have to be read reverse, since the suit is more powerful than the value. 

                           implicit: z = input string
J"KTAZ"                    J = "KTAZ"
             o         cz  orders the hands N of split(z) by:
              _              the reversed of 
               XN+@z1JJ      N, where the values z[1]+J are replaced by J
            e              last element (winning hand)
        xcz)               index of the winning hand in split(z)
       h                   + 1