Open your favorite web browser on any device on your router's network.  Type in the address of your ESP8266 project noted in the previous step into the address bar:

Success, you are connected to the project!  Now to read the temperature, type in the web address (on my network 192.168.0.41) with "/temp" after the address:

Cool!  If you want a more traditional REST response (just the value and not the text telling you it is the temperature), you can edit the appropriate line of the program to remove it.  

Now to ask for the humidity by appending "/humidity" to your ESP8266 project's IP address:

That's it.  You have a ESP8266 module running your own custom code reading a sensor!  No Arduino or other microcontroller needed.