These are the ways I've personally used to get more experience in Service Design and that I found worked well:
Work in a consultancy
Working in an agency is great because you'll get to work on a ton of different projects in a small amount of time. The agency culture isn't always the most healthy, but you'll get a lot of real-world experience, plus you get paid for it.
Volunteer to improve an existing non-profit service
You can help a local NGO to improve its service. For example, by doing a little research project for them or trying to improve things in the backstage to improve their efficiency. Here, you'll learn a lot about the political side of things and how to bring change in complex organisations.
Build your a service, startup idea or side project
Build something by yourself or with a few friends. Here, you'll learn to build something from scratch, and you can really use your full toolbox.