What you need to do is:
Get 2 tumblers/buckets
One should be empty and one should have the new coolant in it.
Now all you need to do is disconnect the transparent reservoir tubes
put the tube carrying liquid into the loop in the new coolant tumbler and the one carrying liquid out into the empty tumbler.
Start the rig till all the old coolant is out and the new coolant just starts to come into the empty tumbler now full of old coolant.
Stop the rig. and plug the pipes with a stop cork.
Empty the reservoir of all the old coolant , fill with new coolant and attach the pipes.
It's a little tricky job but if the stop corks are on one end then the coolant wont drain 'cos of a vacuum.
That's it, put the reservoir back in and start the rig.
Although if I were you, I'd first clean out all the rigs parts, apply new TIM , blow out the dust etc etc etc.
The liquid loop will need to be cleaned with mild battery acid aka distilled water.
That removes all remnants of residue and the gooey stuff.