It's never an easy choice.  
 
Cervical dislocation via broomstick method.. is usually the easiest for beginners. Sometimes the head pops off. There will be lot's of rapid flapping as an automated response that is not indicative of consciousness. Wringing the neck.. as described by a grandparent.. was extremely difficult to do and not effective. 
Tree branch lopper will also do it. See link for examples..
https://bitchinchickens.com/2020/11/12/humane-euthanasia-for-chickens/
Swollen joints can be indicative of certain avian diseases.. consider refrigerating and sending in for necropsy.. Contact info..
Oregon Department of Agriculture
Animal Health Laboratory
635 Capitol Street NE
Salem, OR 97301 US
503-986-4686
fax: 503-986-4688