I was about to go into a detailed ramble about how to do it smoothly, but I think simpler will probably be better for you to learn by.
What you're gonna want to do is set the trigger condition of your event to Auto-Start so that it automatically plays the event. This will also loop the event though, so to close it, you need to do one of two things. Either use the Erase Event command after your dialogue (this will not permanently erase the event though, the event will reset if you leave the map and come back), or use the Switch Operations command to turn on a select switch. If you use the switch method, be sure to click the New Page button up top with the selected switch as a precondition and no trigger condition.