I want to multiply two columns in a pandas DataFrame and add the result into a new column

I think an elegant solution is to use the where method (also see the API docs):

In [37]: values = df.Prices * df.Amount

In [38]: df['Values'] = values.where(df.Action == 'Sell', other=-values)

In [39]: df
Out[39]: 
   Prices  Amount Action  Values
0       3      57   Sell     171
1      89      42   Sell    3738
2      45      70    Buy   -3150
3       6      43   Sell     258
4      60      47   Sell    2820
5      19      16    Buy    -304
6      56      89   Sell    4984
7       3      28    Buy     -84
8      56      69   Sell    3864
9      90      49    Buy   -4410

Further more this should be the fastest solution.