Nice question. But it is very broad.
Because each social media channel is unique and gives different user experience than others. To use them for business with a 0$ budget, you need to be pro user of all of them. Otherwise, paid option is always available for all.
Although, one interesting resource I have from SEMRush. By following this you will be able to generate business leads with 0$ budget via LinkedIn.
If you are still interested in Facebook or Twitter marketing then here are some important things you need to remember.
1) Become a thought leader by sharing insightful content regularly
2) Get in touch with industry influencers and ask them to share your website or blog content
3) Find your targeted audience query and solve it publicly
4) Interact by reply, like or comment on competitors
If you're not able to these all then the best option is to choose social media marketing partner.