Answering my own question.
curl -X GET --basic --user username:password \
https://www.example.com/mobile/resource
curl -X DELETE --basic --user username:password \
https://www.example.com/mobile/resource
curl -X PUT --basic --user username:password -d 'param1_name=param1_value' \
-d 'param2_name=param2_value' https://www.example.com/mobile/resource
POSTing a file and additional parameter
curl -X POST -F 'param_name=@/filepath/filename' \
-F 'extra_param_name=extra_param_value' --basic --user username:password \
https://www.example.com/mobile/resource