When you're in the search page, you can choose your move-in and move-out dates using the search filters. The results will then show you places that are available during that time period.
If you didn't add your move-in and move-out dates to your search filters, you can check if a place is available in each listing. Go to the fixed booking bar at the very bottom of your screen and simply click on the blue button on the right that says "Check Availability".
A calendar will appear with the available dates in black and the unavailable dates in grey. Finally, you just need to click on your move-in date first, and then on your move-out date.