A two part-tariff is a pricing system which looks to extract as much consumer surplus as possible. The total payment made by a consumer is of a form t = F+pq where F is a lump-sum fee tagged along to the usual (price x quantity) payment.
It has been a long time since I've touched this so I'd get a second opinion but -- intuitively, you have a constrained optimisation problem: Let t = total payment by consumers. Choose t,q to maximise t-q such that consumer surplus=0.