To test if it is operate properly, simple apply 3.3v to VCC and GND, and connect CH_PD to VCC.
The module will run and setup a WiFi AP, named ESP_XXXXXX. You can use a mobile phone to scan the AP, and connect. That means your ESP8266 module is up and run properly.
Then connect it to PC with FTDI (USB-Serial interface). Make sure it's work on 3.3V, or a voltage level converter is need.
I have two devices wifi connected to the AP of ESP8266 in CWMODE 2; a mobile phone (IP: 192.168.4.100) and the PC (IP: 192.168.4.101) runnig the test. I tried to ping other devices from the PC, only the AP of ESP8266 (IP: 192.168.4.1) can be ping, the another connected mobile phone (IP: 192.168.4.100) cannot be reached!
That's my very first test on a brand new ESP8266-01 WiFi module, with everything factory default setting.