AHV and self-employment (Zurich)

Hi all, I'd appreciate some insight. I have been unemployed for the past 6 months plus but have worked sporadically as freelance graphic designer (declaring all earnings to syndicom- my unemployment agency). Now I will become part freelance and part self-employed, depending on the contracts I acquire.
Can anyone enlighten me on how officially work both status' (freelance/self-employed) – for example with paying my AHV, and what's the course of action I need to take.
Thanks a lot for any help.