We can go to Workflow screen and create a Workflow (I am using example of Opportunity Sales Process and stages which come with CRM 2013 Online trial)

We will first go to Settings->Process->New

Click on save . Now we start configuring the steps. We will configure the workflow for Record fields change and Click on Select:

Select the following field(As I am sending notification when record is moved to close stage)

Note: You can also configure notification when user switches Process if you Select Process in the above selection instead of stage.

Now, we will click ok and start configuring steps:

We will click on Add Step and Pick Check condition:

Click on Condition and fill the fields like suggested in the below screenshot:

Note: Please mention stage name in CAPS , else it will not work.

Now, Please click Save and close, and select a step for when condition is true. In our case, I will send a notification email to creator of opportunity, hence will pick the step for Send Email:

You can now click on Set Properties and set properties as mentioned below:

Click on Save and Close here and on workflow and Activate workflow:

Note: In case you want to send notification synchronous, you can convert this workflow to Real time workflow.

Now lets try it, Once i move stage of Opportunity to Close, Email is created for me!

Hope it helps!