For a certain column, if you don't care about the ordering, use this
df['col1_num'] = df['col1'].apply(lambda x: np.where(df['col1'].unique()==x)[0][0])
If you care about the ordering, specify them as a list and use this
df['col1_num'] = df['col1'].apply(lambda x: ['first', 'second', 'third'].index(x))