First, you will need four of these:
https://www.sparkfun.com/products/9264
Just use the red and blue anodes and the common cathode.
Then, you will need to calculate the correct resistor to use in order to step down the current so they don't burn out prematurely:
LED calculator for single LEDs
The specs on these diodes are:
Forward Voltage (RGB): (2.0, 3.2, 3.2)V
Max Forward Current (RGB): (20, 20, 20)mA
The next part isn't easy. You will have to find the TX indicator LED on the schematic and use that as your source for getting power to the red/blue anodes.
http://www.cbtricks.com/radios/galaxy/dx2527/graphics/dx2527_sch_new.pdf
I would first wire all four of the red LED in parallel to the TX indicator source voltage on the board. You will have to use a voltmeter and determine how much voltage is there when it is 'on'. Then using the LED calculator, find the right resistor and put one resistor on each anode and wire them in.
Same goes for the blue LED with receive.
This is perhaps
a bit too complicated for a beginner.
In fact, I wouldn't do this until you are sure to act;
there is more to it than I have outlined here.
If in doubt, let a reputable shop do it for you.
Disclaimer: You take your own risks if you do this . . .