I believe the marketing company were on retainer by a number of web agencies, and when they found a lead, they referred it to the most appropriate agency (for a percentage commission) - the agency then continued the sales process (e.g. with a pitch, an RFP response, etc).
I suspect there are a few reasons this model worked:
* The marketing company maintained their database over the long term, so they could discuss previous developments, plans the customer was making, etc.
* Providing leads to a number of web agencies (rather than each agency having a small in-house telemarketing team) gave the marketing company a greater economy of scale, which meant they could afford to invest in tools and training that were specific to telemarketing.
* Providing leads to a number of web agencies allowed the marketing company to generate revenue (commission) from a more diverse set of needs, e.g. sharepoint projects to one agency, wordpress projects to a different agency, etc. If a small agency were doing their own telemarketing, their conversion rate would generally be lower, because they would end up missing out on potentials leads, from not having a particular specialisation.
Depending on what you're doing, you can Google businesses that need help, get their contact details, and go to town. See a business with a busted site? Check for their contact details, call them up or email them, try to get a response, convince them of why they need you to build them a better site.
Cold call.