I don't know how you freelancers and contractors do it.

Gotta make and maintain connections

Connections and reputation are the main components for successful freelancing. I started out with advertising my services on all kinds of freelancing hubs like fiverr or upwork, and of course on my LinkedIn. You can also tell your friends, family members or people you meet at other occasions like meet ups or conventions. From then on it's just maintaining a good relationship with everyone. Clients will eventually recommend you to their colleagues, friends will refer people they know, etc.

Don't be afraid to advertise yourself, but don't be annoying about it either.