There are different kinds of technical writing, differing in the "technical" part. The logical place for you to start, coming from a programming background like I did, would be with programmer-facing documentation: APIs, SDKs, and the tutorials and guides that go with them.
If any of your current (programming) work could benefit from either external (interface) or internal (design, architecture) documentation, you could start there to build your skills and portfolio (and maybe your first gig). Failing that, instead of doing mock work to show what you can do, why not do real work for the open-source project of your choice? That may also help you with the networking; when you contribute valuable documentation to Project Whatever, then (1) your stuff gets seen and (2) the other people working on Project Whatever might help you find paying gigs.
You can also go the professional-association route. STC (Society for Technical Communicators) is the common one, but it's a broad base -- you'll find some programming writers there, but also a bunch of people documenting UIs, hardware, and -- surprise :-) -- non-software products like medical and engineering devices. So it's a broad group, and how deep it is depends on the folks in your local chapter. I gave a talk on API documentation at a regional STC conference a while back and it was the only programming-related topic on the docket; however, a few years later at the national conference there were more options. It varies. I'm not currently a member of STC so I don't have the current sense of it. I found more value in the documentation SIGs of ACM and IEEE, though I've also let those memberships lapse. (Sorry, just lazy I guess. :-) )
Breaking into any new field has two key parts: demonstrating good skills and finding the right people to demonstrate them to. If you can ease into it in your current position then you have a leg up; you already know the people. If not, you have to build a body of work and do some networking.