I imagine them like a subscription service - sign up to a level of service on a per month/year basis and get a certain level of mileage/size of car whenever you request it via an app
I kind of hope that they will be priced like this, because it would solve the main problem of car sharing for me, the marginal cost of a journey. Currently I own a car, and in my head it costs nothing to make a short journey, as most of the costs are fixed overheads. I now do low mileage, usually drive weekends only, and live centrally in a city, so would be a perfect candiate for a car club. But I know I wouldn't pay £13 to rent a car for two hours to go to Asda, whereas I do regularly use my own car for that. Even though using a car club would save me money, on average over a year, as an alternative to owning, the behavioural finance issues in consuming car services that way make it unattractive to me.
Unfortunately, I don't think the subscription idea makes sense. A subscription service can't be cheaper than a taxi service that charges a market price for time of day, because it would make a loss. So, if it can't charge market prices, it can only be more expensive. Which would mean canny users would prefer a pay-as-you-go service.