We have a new project engineer that I recently trained on steps to take for problem-solving and asking good questions. The person was struggling to take ownership of assignments and was relying too heavily on co-workers and his supervisor to solve problems for him. This is an outline of what we went over, you may find it helpful for yourself, or for training new team members on how to solve problems.
This is an example of a checklist that I use for training and on-boarding of new hires. The checklist should be tailored to the position and department of the new hire.