The cheapest WiFi modules on the market (around $3 each) are the ESP8266-01 boards, which are WiFi enabled microcontrollers in their own right (with limited I/O), or they can be used with an Arduino as the WiFi interface. However, they have a funky 2×4 header that is not breadboard friendly.
Here is one possible solution. A inexpensive 2×4 to breadboard converter with a 2×4 socket on top and headers on bottom that match up nicely with a breadboard. It not only works with the ESP8266-01, but also works with the nRF24L01+ RF modules as well.
Now it’s very easy to experiment with these handy modules. If you need a 5v to 3.3v regulator and level shifting for your ESP8266-01, check out these converters!