Wait for late winter to early spring, when the fishhook plant gets ready to resume active growth after winter dormancy. You can also cut the plant when it first resumes growth after dormancy. While you can cut in summer, it's less desirable.
Rub a sharp knife or razor with a cotton ball dipped in rubbing alcohol to sterilize the blade. Avoid using scissors or pruners since this can crush the soft tissue inside the fishhook stem.
Cut a section of stem using your sterilized razor or knife. How much you want to cut is up to you, and depends on your purpose. If you want to grow new plants from the cuttings, take a cutting of several inches. If you are only trimming the fishhook plant to keep long tendrils off the ground, you can cut as little as you need. In general, avoid cutting off whole shoots if you're making cuttings, as these can be tricky to root.
Take as many cuttings from your fishhook as you need. When you finish, re-sterilize your knife or razor with rubbing alcohol.