Specify the ncol parameter in legend. In your case something like:
plt.legend(loc="lower left", ncol=len(df.columns))
This is the only line I changed in your script.
Working full code:
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
# data
np.random.seed(123)
x = pd.Series(np.random.randn(100),index=pd.date_range('1/1/2000', periods=100)).cumsum()
y = pd.Series(np.random.randn(100),index=pd.date_range('1/1/2000', periods=100)).cumsum()
z = pd.Series(np.random.randn(100),index=pd.date_range('1/1/2000', periods=100)).cumsum()
df = pd.concat([x,y,z], axis = 1)
# plot
ax = plt.subplot()
for col in (df.columns):
plt.plot(df[col])
plt.legend(loc="lower left", ncol=len(df.columns))
plt.xticks(rotation=90)
plt.show()