Retrieve a Customer's Subscription ID from Stripe
The relevant part of the Stripe API reference suggests that upon retrieving a customer you will have access to a subscriptions attribute containing a url at which you can access a list of subscriptions.
However, on creating a subscription, Stripe will return the subscription to you with the subscription id. I would suggest storing this in your database as an attribute on the customer model (if they will only have one subscription) or, and the method I use, is to have a Subscription model in my database which stores some of the frequently accessed data and avoids pinging the Stripe API too much.