I'll try - at least, this is how I understand it from everything I've read, including quite a lot of sources in their language.
In theory, the idea is that the workers appointed the managers and that their salaries depended on the performance of the workplace. So - for instance - a successful coal mine would pay more, while a struggling coal mine would be forced to shut down because they didn't adapt their working practices to become successful. The government (or republic Government, or local government, whatever) would help to create workplaces according to the needs of the country, which in turn would be run by the workers. The end result is that you have a very democratic workplace, because bad managers would be removed while successful ones would be rewarded by the workers who were rewarded themselves by the success of the company.
In reality, it didn't work like that. Managers still came from the LCY (League of Communists of Yugoslavia), and workers tended to threaten strikes (which would bring down managers) unless their demands were met. What happened in the end was that because managers wanted to keep their privileged positions, they gave in easily to the demands of workers, which in turn meant widespread financial mismanagement and abuses.
I think at least part of the idea was that successful managers would then rise in status within the LCY, which in turn meant a rise in their own political power and hence the leaders of the country would have risen from ordinary worker to manager to successful politician. The reality is that the workers councils responsibility for appointing managers were never really given independence - and managers rose in prominence politically according to their skill in politics and not according to their success in business.
I remember one reason why Yugoslavia was in such a mess by the 1980's was because large companies (for some reason...) had the ability to sell promissory notes without any real checks on what they were doing. Because of the theoretical idea of worker self management, these bosses would run up ridiculous debts without any control, which in turn paid for paying higher and higher salaries and providing things such as kindergartens and transport for workers. The reason they got away with it was because Yugoslavia was decentralised in the mid 1970's, so local Party bosses couldn't really care less if Company A from Bosnia was screwing Company B in Serbia as it meant that Company A was increasing living standards.
It's also worth pointing out that Yugoslavia was heavily reliant on exporting labour and receiving remittances, which helped to prop up the Yugoslav economy.