Best way is to use Panda’s to_csv() built-in function
df.to_csv('filename', index=False)
Don’t forget to pass index=False as a second parameter if you don’t want index row saved as a column (in other words use it if you don’t want duplicated index when opening the file again).
By the way, you can also withhold column names when exporting csv with header=False:
df.to_csv('filename', index=False, header=False)