DSM has the accepted answer, but the coding doesn't seem to work for everyone. Here is one that works with the current version of pandas (0.23.4 as of 8/2018):
import pandas as pd
df = pd.DataFrame({'col1': [1, 2, 2, 3, 1],
'col2': ['negative', 'positive', 'neutral', 'neutral', 'positive']})
conversion_dict = {'negative': -1, 'neutral': 0, 'positive': 1}
df['converted_column'] = df['col2'].replace(conversion_dict)
print(df.head())
You'll see it looks like:
col1 col2 converted_column
0 1 negative -1
1 2 positive 1
2 2 neutral 0
3 3 neutral 0
4 1 positive 1
The docs for pandas.DataFrame.replace are here.