You'll then want to select the menu items for the ESP. Thanks to Hackaday, here are the steps:

When you have the ESP8266 support installed you can then select the Generic ESP8266 as a board.

From the Tools -> Programmer menu item, select esptool

With your project powered and the USB to serial cable plugged in, you will need to select the serial port which the cable shows up as.  On Windows, use the "Devices and Printers" Control Panel view to see the cable.

Now you should be able to compile the program loaded on the last page.  Click the round Check icon to make sure the program compiles.  

If you have errors which mention DHT then your Adafruit DHT library was not recognized (go back and follow the install steps again).  

If everything is set, the program will compile ok: