arduino pro mini downloading?
The Arduino Pro Mini has a row of connections at the small end that align with the connections on the USB-to-Serial board you have.  They are marked GND - VCC - RXI - TXI and should be in the same order as the connector on the FTDI board. I think that the pin marked GRN on the Arduino will align with the connector marked DTR on the USB-to-Serial board, but please make sure that VCC aligns with 5V!

With the FTDI board plugged into the Arduino, you can plug your computer into the FTDI board's USB port and when you run the Arduino IDE programming tool, that USB port should say that it's connected to a serial port.  Pick the "Arduino Pro or Pro Mini" as your board, then pick your processor (most likely the "ATmega328 (5V, 16MHz)" and finally your port (that serial port you found).

Now when you upload your Arduino program to the Arduino, it will know the board your have and the port to use.

As for programs to use, start simple and get the onboard LED to blink.  From there, you'll have the basics down for creating a program and getting it to the Arduino.  You'll find tons of example programs (called sketches in Arduino land) that will help you connect all your fun wireless gizmos!

As noted above - Google is your friend.  There are many places to go for examples and help.  Start with some of the commercial sites like Adafruit and SparkFun. Their staff really supports the Arduino community with how-to videos, libraries, examples, etc.