This is not intended to be a difficult answer. It's just that it depends, really, on the project and the data source that you're talking about.
For example, the Facebook dataset was acquired by Aleksandr Kogan using apps from Facebook. Other datasets were acquired, some at the instigation of the owners of those datasets. For example, clients would sometimes provide the company with information, so they would help that modelling process.
In other cases there would be a contractual relationship directly with a company—a data vendor that sells consumer data, for example, or a company that sells its customer lists.
In other cases, subcontractors would be used to go and acquire data generally, depending on what they would go and find. For example, AggregateIQ was sometimes tasked with finding datasets for particular projects. They did that in Trinidad, for example. They went out and acquired data on behalf of the company.
Sometimes it's a contractual relationship directly with the data vendor. Sometimes it's an application that collects data. There are a lot of different ways you can collect data.