At the moment, if you want to petition Parliament, you have to collect physical signatures on paper forms. Nowdays, petitions are largely done online, and so this is circumvented by having a petition of one person, asking that the House take note that so many thousand other people have signed an online one. But it looks like change is finally brewing, with Leader of the House Chris Hipkins introducing a motion for a sessional order to allow Parliament to receive electronic petitions:
A lot will depend on the specific requirements imposed by the Clerk, but it is likely that this will make the petition system significantly more accessible than at present. Hopefully it will be introduced soon.
(And then we'll need the next step: a formal system like that used int he UK or US to force Parliament to debate issues raised if enough people petition it).