Know how to bleed the brakes? Flushing is just like that except...
Get a turkey baster & then never put it back in the kitchen...
Suck the old fluid out of the MC because that's where it has picked up moisture & crud. Then push/twist the pistons in to make room for the new pads. Suck out a little more fluid.

Fill the reservoir with fresh fluid. Bleed the brakes, but you don't stop when the bubbles are gone. You keep going until the fluid coming out of each caliper is nice & clean & fresh. Maybe 1/2 liter from each rear, a bit less from each front.

Got ABS? If it's got a separate reservoir, I think I've posted (somewhere) how to bleed that.