I think your idea is excellent. Even with minimal German knowledge, you could help someone. And since you expressly intend to improve your language skills, so much the better.
In Zurich, the organisation http://www.nachbarschaftshilfe.ch/
(in English "Neighbourhood help") keeps lists of people who can offer help, and anyone can appeal for helpers, there. The help is given and received entirely free.
There are a dozen or so community centres, run jointly by the City of Zurich and pro juventute (an organisation for the youth). They offer many groups, courses and meet-ups for children, young people and adults. Some are run by a paid staff member, but many of the projects there also need volunteers. http://www.gz-zh.ch/
Here is the part of the Red Cross that coordinates private people to visit other private people at home, or to escort them to doctor's appointments, for example. Some volunteers do this by car (and are paid a small petrol allowance), others go by public transport. https://www.redcross.ch/de/srk-diens...gen-Einsamkeit
Some hospitals have volunteers who receive guests and show them their rooms, etc. and probably you would need German for that... but it would be worth finding out if there is a need, particularly, say, at the Universitätsspital or Waidspital for helpers for English-speaking patients.
If you are interested in ecological matters, you could join a collective project like http://www.ortoloco.ch/photologue/gallery/page/1/
, which grows its own vegetables.
Or get in touch with those around the Urban Gardening project at the ETH Zürich https://www.ethz.ch/content/dam/ethz...nal_report.pdf
Of course, you could always try posting on this forum, asking if anyone would like any help from you, for example in exchange for practicing German or for help with any other aspect of your integration process. If you'd like to do than, then it would be good if you would list the kinds of skills you would like to share.
One of the main ways to get to know people where you live is to join a club or society (known in German as "Verein"). The municipality office (Gemeinde) where you live can usually give you a list of the main Vereine in the area. Those Vereine have regular meet-ups for their particular activity, and generally welcome newcomers willing to share and to learn, and sometimes also have social events beyond the actual meetings.