Twilio developer evangelist here.
Best place for you to start would be the Python making calls quick start. Follow that tutorial through and you should understand how to make a call with Python.
Though, as you say, the key is the POST request to the calls resource. It's easiest to perform this using our Python helper library and looks a bit like this:
from twilio.rest import TwilioRestClient
# Get these credentials from http://twilio.com/user/account
account_sid = "ACXXXXXXXXXXXXXXXXX"
auth_token = "YYYYYYYYYYYYYYYYYY"
client = TwilioRestClient(account_sid, auth_token)
# Make the call
call = client.calls.create(to="+14085551234", # Any phone number
from_="+12125551234", # Must be a valid Twilio number
url="http://twimlets.com/holdmusic?Bucket=com.twilio.music.ambient") # Just plays hold music
Let me know if that helps at all.