You need to select that column:

In [41]:
df.loc[df['First Season'] > 1990, 'First Season'] = 1
df

Out[41]:
                 Team  First Season  Total Games
0      Dallas Cowboys          1960          894
1       Chicago Bears          1920         1357
2   Green Bay Packers          1921         1339
3      Miami Dolphins          1966          792
4    Baltimore Ravens             1          326
5  San Franciso 49ers          1950         1003

So the syntax here is:

df.loc[<mask>(here mask is generating the labels to index) , <optional column(s)> ]

You can check the docs and also the 10 minutes to pandas which shows the semantics

EDIT

If you want to generate a boolean indicator then you can just use the boolean condition to generate a boolean Series and cast the dtype to int this will convert True and False to 1 and 0 respectively:

In [43]:
df['First Season'] = (df['First Season'] > 1990).astype(int)
df

Out[43]:
                 Team  First Season  Total Games
0      Dallas Cowboys             0          894
1       Chicago Bears             0         1357
2   Green Bay Packers             0         1339
3      Miami Dolphins             0          792
4    Baltimore Ravens             1          326
5  San Franciso 49ers             0         1003

Use boolean indexing and pass the condition:

In [155]:
df[df<1] = 0
df
Out[155]:
     0    1
bar  1  0.0
foo  0  0.0
qux  0  4.1

Just to show what is happening here performing df < 1 will return a boolean index:

In [156]:
df < 1
Out[156]:
         0      1
bar  False   True
foo   True   True
qux   True  False

This we then pass to df as a mask and can then assign the new values as df[df<1] see the docs for further examples