I've posted this a gazillion times I think:
Download the Optiloader sketch into your Uno:
Put your new part on a solderless breadboard, with 16 MHz xtal, 22 pf caps, 10K reset pullup resistor.
Connect Uno's +5 to VCC/AVCC pns, Gnd to Gnd, D13 to D13, D12 to D12, D11 to D11, Uno's D10 to blank chip's reset.
Or make these connections to your standalone board if there is no conflict on the pins.
Run the sketch, see the video in this thread:
http://arduino.cc/forum/index.php/topic,68183.0.html
Put newly bootloaded part in your Uno and download a sketch, or download on your new hardware if it supports that, maybe using an FTDI Basic or CP2102 USB/Serial adapter if not.