Here’s a way to program an Arduino wirelessly while still using the stock IDE. It uses an alternative bootloader called SuperDuplex along with an IR receiver like the ones used for TV remotes.

Despite a wealth of tutorials for setting up and writing code for the ESP8266 WiFi module, there has not been much of anything on programming this cheap wireless module with the Arduino IDE ...

Although Arduino's programming language is based on C++, you won't be able to use all of its commands. But, you can still use objects in Arduino's IDE, which are a fundamental aspect of C++.

For beginners learning to program Arduinos, a web-based, fully networked developer environment called Codebender could drastically reduce the learning curve.