Competing in this category when there are so many dominant incumbents is really difficult. You'll need a product that significantly leapfrogs that of the existing leaders, which means it's likely mobile-first and focuses on a simplified, minimalistic user experience that delivers on the core use case of these apps.

To answer your question as you asked it:
1) Build the best product in the category;
2) Find a few key reference users (Social Media Managers at known companies who are themselves influencers about social media management) who are willing to declare your product as better than anything else;
3) Make it easy for enterprises to adopt this and establish some use cases that demonstrate how the more users who use this within a group or enterprise, the better their business results are vis a vis social media.
4) Buy inexpensive ads (Twitter is likely best) promoting these case studies encouraging sign-ups.
5) Talk to everyone who signs-up and hold their hands and lead them to become advocates for your service AND paying customers.

The challenge is that customer acquisition costs or even lead costs are high, driven up by the significant cash that the incumbents can afford to spend on acquiring new users & prospects.

Virality has proven difficult to achieve in this product category so it's really a function of convincing users to flee their existing tool in favor of an unknown, unproven product.

Happy to talk to you in detail in a call.