You will need to be a workflow admin on the workflow itself or have the Full Write Workflows permission to perform this action.
Navigate to the workflow you would like to add a new process to. Then select "Add new process" from the "Actions" menu in the top right.
You can also click on "+ Add a process" at the bottom where the processes are listed.
A pop up will appear with the following fields:
Name - the name of the process. This must be unique within the workflow.
Description - a brief description on what this process does.
Reentry Buffer - how long to wait after a person reaches the "Done" status before they can be added to this process again.
Triggers - optional trigger which automatically adds a person to the process when specified conditions are true. See this article for more details on triggers.
Once you are done. click on "Create" to add the process to the workflow.
Security
Process managers are users who have full admin rights to a specific process. Any admins on the associated workflow already have full admin rights to any processes within the workflow so there is no need to also add them as process managers.
You will need the either have Full Write Workflows permission or be an admin on the workflow containing the process you would like to add a manager to.
To add a new process manager, go to the process and select "Add manager" from the "Actions" drop down menu in the upper right.
A pop up will appear where you can search for the person to add. Once done, click on "Add" to finish adding them to the process. You can have as many process managers as you would like. To remove one, click on the "X" button next to the manager you would like to remove.
Read this article for more information on controlling access to the processes.