Go to your Google Calendar
Click on the day and time you want to start a new Meeting/Appointment/Event.
A new pop up window will appear
Click on 'More Options' on the bottom right. This will redirect you to the 'Event Edit' page.
On the Event Edit page click on the Find a Time link (#1)
Next enter in the name(s) of the people that you would like invite to the Meeting/Appointment/Event (#2).
On the left hand side of the Event Edit page you will see the times the people you would like to invite to the Meeting/Appointment/Event are available and when they are not.
(In the example above we can see Erik, Justin and I all have free time to meet between 1 pm to 2 pm on the 31st)
When you are done click the Save button at the top of the page. Emails will be sent to the folks you invited alerting them to your Meeting/Appointment/Event request.