There are likely several ways to the same end point so others may chime in...
Use fresh brake fluid. The fluid is hygroscopic; it absorbs moisture from the air so any old leftovers may be contaminated due to poor sealing of the original container.
I used a small kitchen baster thingy -squeeze bulb atop a graduated plastic tube- to extract most of the old fluid from the brake reservoir. A shop towel absorbed the rest, leaving only what was in the brake lines.
I then slowly added fresh fluid to the fill mark, being careful not to disturb what was in the lines nor get any fluid on painted surfaces.
After that, it's business as usual for attaching a bleed hose, opening the bleed valve, stroking the lever, closing, refreshing the supply, blah, blah, blah...
With a clear vinyl tube from the bleed valve poked into a clear glass container, just watch for the fluid to go from dirty to nice as you pump out the nasty old liquid.
BTW, after final top up of the reservoir and replacing the cap, some like to use a strong rubber band to hold overnight brake pressure as an aid in getting rid of those small pesky air bubbles that tend to remain in the lines.
Monte