In a speech in Liverpool this morning, Cameron said groups of "vanguard" projects in Liverpool, Eden Valley in Cumbria, Sutton in London and Windsor and Maidenhead would be given an organiser and a team of civil servants from the Communities and Local Government department to help them with their work and to break through bureaucratic obstacles.
The projects in Liverpool include a scheme to recruit volunteers to work in museums, and those in Cumbria include a local group that is attempting to take over its community centre.
In his speech, Cameron said community groups in the four areas had approached the government and asked it for support. He said similar support would be available for other groups that got in touch to ask for help.
"I want other people to come forward and ask for the same support," he said. "If you want to improve your local area, tell us what you want to do and we will give you the tools to make it happen."
Cameron did not say how much the government would spend on the local projects, or how much funding might be available to other groups.
He said he wanted charities and social enterprises to play a greater role in delivering public services because this would encourage innovation.
Stephen Bubb, head of chief executives body Acevo, warned that the government would have "a job on its hands to close the gap between its heady rhetoric and current reality".
He said the devolution of power to local authorities could mean councils seeing voluntary organisations as easy targets for cuts rather than allies in building a big society.
"David Cameron has described cutting the deficit as his duty and building a big society as his passion," he said. "The challenge for him will be to ensure that his colleagues in central and local government share that passion, and don't carry out their duty in a way that inadvertently stymies it."