To do a flush you simply disconnect your return line from the power steering reservoir and drain the thing. Then stick a long clear 3/8"OD tube into the return line and run it down to a empty 2-liter soda bottle. Use some tape to secure the hose into the bottle so it can't fall out when fluid comes squirting out.
Once you're ready, turn on the car and steer the wheel back & forth until you can no longer turn the wheel (the pump will get loud when it sucks air). This forces the old fluid out into the soda bottle. Have the bottle and hose secure cause it comes out with a bit of force. Sucking air into the system is perfectly fine and no damage will be done to anything.
Now re-connect your return line to the reservoir and fill it with fresh fluid. Start the engine and steer back & forth, then get out and top off the reservoir. Do this a couple times until the fluid level stays topped off. You can also have an assistant in the car steering back & forth as you add fluid. The pump may still make noise until you finally shut the car off and let the foamy fluid settle. This allows tiny air bubbles in the fluid to collect into large ones. Then the next time you start, they will get pumped back to the reservoir for good (noise for only a short period when you 1st start the car)
If you want to really get all the old fluid out, you can repeat this entire process twice and flush your new cleaner fluid one more time. This will really clean out the system, but it's probably unnecessary.
1 flush requires at least 2 bottles of Honda PS fluid
2 flush requires about 4 bottles of Honda PS fluid
Honda Power Steering Fluid Change - YouTube