I have read a csv file and pivoted it to get to following structure:

pivoted = df.pivot('user_id', 'group', 'value')
lookup = df.drop_duplicates('user_id')[['user_id', 'group']]
lookup.set_index(['user_id'], inplace=True)
result = pivoted.join(lookup)
result = result.fillna(0) 

Section of the result:

             0     1     2    3     4    5   6  7    8   9  10  11  12  13  group
user_id                                                                      
2        33653  2325   916  720   867  187  31  0    6   3  42  56  92  15    l-1
4        18895   414  1116  570  1190   55  92  0  122  23  78   6   4   2    l-2 
16        1383    70    27   17    17    1   0  0    0   0   1   0   0   0    l-2
50         396    72    34    5    18    0   0  0    0   0   0   0   0   0    l-3
51        3915  1170   402  832  2791  316  12  5  118  51  32   9  62  27    l-4

I want to sum across column 0 to column 13 by each row and divide each cell by the sum of that row. I am still getting used to pandas; if I understand correctly, we should try to avoid for loops when doing things like this? In other words, how can I do this in a 'pandas' way?

Try the following:

In [1]: import pandas as pd

In [2]: df = pd.read_csv("test.csv")

In [3]: df
Out[3]: 
  id  value1  value2  value3
0  A       1       2       3
1  B       4       5       6
2  C       7       8       9

In [4]: df["sum"] = df.sum(axis=1)

In [5]: df
Out[5]: 
  id  value1  value2  value3  sum
0  A       1       2       3    6
1  B       4       5       6   15
2  C       7       8       9   24

In [6]: df_new = df.loc[:,"value1":"value3"].div(df["sum"], axis=0)

In [7]: df_new
Out[7]: 
     value1    value2  value3
0  0.166667  0.333333   0.500
1  0.266667  0.333333   0.400
2  0.291667  0.333333   0.375

Or you can do the following:

In [8]: df.loc[:,"value1":"value3"] = df.loc[:,"value1":"value3"].div(df["sum"], axis=0)

In [9]: df
Out[9]: 
  id    value1    value2  value3  sum
0  A  0.166667  0.333333   0.500    6
1  B  0.266667  0.333333   0.400   15
2  C  0.291667  0.333333   0.375   24

Or just straight up from the beginning:

In [10]: df = pd.read_csv("test.csv")

In [11]: df
Out[11]: 
  id  value1  value2  value3
0  A       1       2       3
1  B       4       5       6
2  C       7       8       9

In [12]: df.loc[:,"value1":"value3"] = df.loc[:,"value1":"value3"].div(df.sum(axis=1), axis=0)

In [13]: df
Out[13]: 
  id    value1    value2  value3
0  A  0.166667  0.333333   0.500
1  B  0.266667  0.333333   0.400
2  C  0.291667  0.333333   0.375

Changing the column value1 and the like to your headers should work similarly.