Lot cleaner, simpler way to do it- remove the return line from the pump and cap the fitting. If you don't have a cap use a length of hose elevated above the pump reservoir. Attach another piece of hose to the return line, long enough to get it in a bucket or pan. Start/ stop the engine a couple times, it'll run the reservoir dry pretty quick. Repeat till you get nice red fluid coming out and reassemble.
If you get whine out of the system a quick check to see if air is present. Note the fluid level in the res with engine off, then start it. If the level drops there's air in the system, which can be cleared as Troy said by driving a while. Alternatively a Mityvac style vacuum pump can be used to pull the air out. Get a squishy bouncy ball at Walmart or toy store, Superballs are too hard to seal to the irregular surface. Run a piece of brass through it and hook to the vacuum pump, apply 15-20" of vacuum for 5 minutes with the engine running. It'll get louder with vacuum, and if the level's too high fluid will go into the pump. Turning full lock right usually helps.
