Yep, sit a bucket under the steering box & disconnect the fittings so it drains. The key thing you must do after refilling the reservoir is to NOT start the engine until you have bled all of the air out of the lines. The new power steering pump will lkely be ruined if it runs before you have bled all of the air out.
The good thing is that it is easy to bleed all of the air out of the power steering system. Jack the front-end up so the weight is off the front tires. Then fill the reservoir with fresh brake fluid. Next, turn the steering wheel fully left/right 25-30 times. Keep the reservoir level up as it drops while the brake fluid circulates. Caution that the brake fluid level will rise & fall as you turn the steering wheel back & forth so if it's too full, it can overflow and freak you out by making you think it's leaking.
So once you have fully cycled the steering left/right (all the way to the steering stop limits) 25-30 times, then you can start the engine. Cycle the steering some more to finish bleeding it. It may still squeal a little until you drive it but so long as you cycled the steering enough before starting the engine, it'll be fine. Once you stop the engine, check the brake fluid again and top it off if it's down a tad. And make sure to wipe the brake reservoir cap area off so it is clean before removing the cap... you don't want any debris to drop down inside the reservoir.
Good luck... remember to not start the engine until you have bled the air out.