In the WordPress admin go to Products and then click on one of your products
Scroll down to the Product Data tab and right next to the Sale Price click on the Schedule link
Once you click the Schedule link two new fields will popup. The start date and end date.
Click on the calendar icon to open a clickable calendar
Go ahead and enter your dates
Don't forget to press the Update button and then view your product on the front end.
How the Sale Date Works
The sale date is based on the time you have set for your site. That means that if someone is shopping in Bangkok which is 14 hours ahead of where I am (Denver) and it's still Thursday evening my time they won't see the sale.
You can check the time zone set for your site under Settings > General > Timezone.