The 'earlytests' beta branch has been updated with the new Level Editor and the ability to play levels from the Steam Workshop. To opt-in to this beta, right-click Paint the Town Red in your Steam Library, choose Properties and choose 'earlytests' from the dropdown in the BETAS tab.
The Level Editor is a work in progress. Usability and functionality will improve and available content will increase over time, but there are already a lot of possibilities. We're working on an official guide that gives information on the controls and how things work and we'll be updating it with more information and video tutorials over the coming days. Right now the interface for selecting and playing downloaded levels is very basic and temporary as the entire main menu will be replaced in the final release of version 0.7. There will be more information and options for the downloaded levels in the new menu. The ability to play any user created level in co-op multiplayer will also be coming in the final 0.7 release. We're expecting 0.7 to be complete and available within the next 2 weeks. Head into this forum thread for discussion about the Level Editor and post there if you have any questions or find any bugs.