The HC-05, a Bluetooth to serial bridge, can be found for around $5 on the internet and therefore may be the cheapest way to add Bluetooth connectivity to your project.

However, its default settings may need to be changed depending on your application. [Hazim] explains a way to enter the HC-05 AT command mode to benefit from the rich set of features that the device can provide. The process is fairly simple as it only consists of maintaining the key pin of the HC-05 high while powering on. The device then boots in AT command mode with a default 38400bits/s speed and listens for all of the AT command set (PDF). As an example [Hazim] provides a sketch allowing you to write the AT commands directly in your favorite terminal.

With the basics out of your way you may want to further research the hardware, especially if you will be using modules from different sources. They don’t always come with the same firmware.