Fingerprint Scanner -> Arduino
Pin 1 - TX (black) D4 - RX
Pin 2 - RX (white) D5 - TX
Pin 3 - Gnd (white) GND
Pin 4 - VCC (white) +5v
No resistor is necessary for 5v use, regardless of what the sample sketch's suggest.
The sketch uses SoftSerial, so the pins on the Arduino can be changed in the sketch.
You will need to download the examples and libraries, then upload the Enroll sketch to make the unit recognize your finger print. Follow the instructions in the serial monitor, then upload the IDfinger sketch. Now when you scan your finger, the serial monitor will show "Verified" (with the appropriate ID number) or "Finger not found" if it's not recognized. All you need to do is to enable a relay if a correct fingerprint is detected, and possibly write a entry line to a SD card with time and date stamp for a entry log.