The following article refers to functionality available in Workflow builder, which can be accessed in one of the following locations, depending on your configuration:
Administration -> HR -> Workflows 

In Workflow Builder, it is possible to create a workflow that the employee can trigger themselves.  The workflow will need to be of the Category "Task" and Type "Task".

When creating your new Task Workflow, you will see the option for "Employee can trigger". This should be set to "Yes":

How can the employee trigger the workflow? 

Employees can trigger workflows set up in this way by navigating to:

Self service -> My details -> My workflows

This table shows the employee all workflows triggered for them, where they could start the workflow. They can start a new workflow from this page by clicking on the "Start new workflow" button at the bottom of this table.

The employee can then select the workflow from a drop-down list of available workflows, and click Submit to trigger the workflow:

Caution should be used with this option, if the workflow or associated forms contain anything sensitive that you may not want the employee to be able to see.