I have started my way with the arduino UNO, moving to pro mini I didn't buy the USB adapter but used the UNO board to upload my sketches.
Step 1: Removing the Atmel IC
Very cerfuly remove the Atmel IC from the Arduino UNO, the pins are very gentel so be very cerful.
I used a flat driver, twisting it gently from both sides to take it out slowly bit by bit.
Step 2: Connection
Connect UNO's pin 5v to mini's main VCC pin,
UNO's pin GND to mini's main GND,
UNO's pin RX to mini's RXI,
UNO's pin TX to mini's TX0,
UNO's RESET to mini's GRN
Step 3: Load Sketch
Load the sketch to the Arduino IDE, for the example I used the Blink sketch wich is also used for an Arduino first test
Step 4: Set Board
Set the IDE for using the pro mini board,
Tools => Board => Arduino Pro or Pro Mini (5V, 16Mhz) w/ Atmega 328
Step 5: Upload Sketch
Upload the sketch using the regular uploading button.
Step 6: Your Good to Go
You should recive the "Uploading Done" massage in the status bar and you are good to go, sketch uploaded.
Now go make something...