You should find that there is an OOTB of the Process for Problem Management already, which you can start use straight away; however you may find that the process named "Simple Problem" is deactivated and just needs activating.
To view the "Simple Problem" process you will need to access Console and go to Designers > Process Designer > Processes > then expand the tree to get to Problem, then you click on the process and activate this from the Actions box.
Once the process is activated, you can start using this but first you will need to create a shortcut to raise tickets again the process, if you are using Web, this can be via the following method.
> Right click into a Shortcut Group
> Select "Add Process or Object shortcut
> Give a title then select Module = Problem Management: Object: = Problem Lifecycle: = Simple Problem
> Ensure you have ticked "Add to shortcut bar?"
> Press OK.
The OOTB box process is there as a starting point and you can expand this similar to Incident to include many other actions and functions, as a guide please see below link to the Designer guide to how you can achieve this.
Additionally you may wish to raise Problem records directly from an Incident, this can be achieved by using "Optional Actions" at a specific status.
Hope this helps