2002 trailblazer, power steering went out yesterday. I checked reservoir and it was empty so i completely topped off with a new quart. about ten minutes later it went out again and when i checked, the reservoir was bone dry. should i replace the hose and if so how do i know which one?

you have serious [problems, You will need to replace both the high and low pressure hoses , Next check your steering rack. If you believe that strongly about pump replace it. This is not a simple DIY repair, call around for repair price. You will still have steering but it will very heavy and difficult ( good way to have an accident). good Luck

The reservoir is mounted on top of PS pump. (You need to find a new mechanic) Check online parts store for pics of your unit - you'll see pic.

Do you mean that there is a plastic bottle of ATF sitting loose under your hood? Or are you asking what the black reservoir with a knurled cap that is full of ATF is for?
If you are asking about the reservoir that is part of the car, it is the power steering fluid. Car parts stores will try to sell you fluid in bottles that say Power Steering Fluid, but your car uses Dextron ATF which is the same thing only it is cheaper when you buy ATF by the quart rather than PS Fluid by the pint.
If you have a bottle of ATF, someone probably put it there so it would be handy when they needed to top off the power steering reservoir. Topping off the power steering reservoir is a routine exercise on many BMWs because their power steering hoses tend to leak.

Have you checked your tie rods? Possibility one is either bent or broken, I've seen it before on TB's. That pulley shaft is a common problem to break, especially when cold out. PS pumps/pulley shafts and tie rods will snap if doing donuts in the snow with the steering wheel cranked, or off-roading. The PS is completely mechanical, no fuses or relays.

YOU HAVE A RUPTURE PRESSURE LINE IF YOU HAVE NO POWER STEERING FLUID IN THE POWER STEERING RESERVOIR.LOCATE LEAK THEN BLEED POWER STEERING SYSTEM BY ADDING POWER STEERING TO RESERVOIR.DONT OVER FILL BY FULL COLD MARK ON POWER STEERING DIP STICK.ADD FLUID TO RESERVOIR WAIT A 2 MINUTES.CHECK FLUID LEVEL AGAIN.WHEN POWER STEERING FLUID LEVEL STOP DROPPING.START ENGINE LET IT RUN FOR 10 SECONDS.THEN TURN OFF ENGINE CHECK POWER STEERING FLUID ADD FLUID IF FLUID LEVEL DROPS. WHEN FLUID LEVEL STOP DROPPING.SAFELY RAISE SUPPORT VECHICLE FRONT WHEELS.START ENGINE.NOW TURN STEERING WHEEL GENTLY FROM STOP TO STOP MEANING LEFT TO RIGHT DONT HOLD IN POSITION.LET THE STOP TO STOP BE QUICK.CHECK POWER STEERING FLUID AFTER YOU HAVE TURN STEERING WHEEL ABOUT 7 STOP TO STOP.WHEN FLUID LEVEL STOP DROPPING YOU AT HOT MARK ON DIP STICK BLEEDING PROCESS COMPLETE.TURN OFF ENGINE LOWER VECHICLE BACK TO GROUND WAIT ABOUT 5 MINUTES CHECK YOUR FLUID LEVEL.IF FLUID LOOKS LIKE A TAN COLOR.YOUR POWER STEERING SYSTEM FULL OF AIR.TURN OFF VECHICLE LET VECHICLE SET A LONG WHILE TO AIR BUBBLES SETTLE DOWN LOOK FOR LEAKS AROUND POWER STEERING PUMP FRONT SEAL AND CHECK FOR LEAKS AROUND POWER STEERING LINES.

You really can't flush out the steering system fluid other then siphoning the fluid out of the steering pump reservoir. This is the easy way.
The hard way:
Remove the filler cap from the top of your power steering system then disconnect the reservoir's hose. It should be located on the bottom of the reservoir. The hose can be tough to remove, so make sure you have plenty of patience.

Replace the reservoir's hose with another hose. It should lead to an empty container. You'll use this container to store the old power steering fluid as it leaves the reservoir. Lift the front end of your car off the ground by using a car jack.

Add new power steering fluid to the reservoir. As you add the new lubricant, it will force the old lubricant into the tube you've connected to the bottom of the reservoir.

Climb into the drivers seat and rack your steering wheel back and forth. The wheel should be locked in place, allowing only a slight range of mobility. This will help the extra lubricant within the power steering system to drain.
Watch the empty container. It should fill with old lubricant. Once the old lubricant has been flushed and you see clean fluid replacing it, you've finished the hard part.

Disconnect your hose and move the container. Replace the original reservoir hose. Pour new, clean power steering fluid into the reservoir. Rack your steering wheel a few more times to squeeze out air that might be trapped in the lines. Replace the filer cap and close your done.
Thank you for suing fixya and good luck

check the fluid. if its fine then you probally need a rack and pinion. also check the belt that runs the pump.

may be a bad fuel pump need to check for power and ground at pump

You could have a problem with your power steering, but some simple things to check is to first see if your power steering pump reservoir is full of fluid. If it is low or empty, your steering will suffer, and worse would be the power steering pump will fail if you run it dry too long. If it is low, fill the reservoir, and wipe down the hoses and pump before you start the vehicle, so you can find out a general area of where the leak is coming from.

HI check your power steering oil pump reservoir filter screen this seats at the bottom of reservoir is probably plug .it can cause the pump to aerate if thats your case replace reservoir.for proper inspection of reservoir completely empty it and check. hope this helps.