Water softener beads in the system
Sounds like the riser pipe is broken. Your softener will need to be rebedded (emptied, and then refilled, and obviously a new riser pipe installed). 

To clear out your system, really the only way is the obvious way: flush it out with water. First off, make sure your softener is bypassed until it's fixed, so you don't add to the problem. 

Regular faucets

Take off the aerators, shower heads, and anything else that has a screen or filter in it, and run water until you get everything out. 



Other valves

There's a chance with some valves you could get something caught in them, so if you still notice a reduced flow or leak from a particular tap, you'll have to take apart the valve. How to do this varies depending on each particular valve, but you can find help online (try searching for "replace valve cartridge in ") or ask another question here. 

Hot water heater

The hot water heater is a bit trickier, since you really can't get enough flow through the tank to "flush" it. The only way is to drain the tank:


Turn off water inlet valve and power/gas
Open some hot water taps in your house -- this will let air back in so the tank can drain
Connect a drain hose to the bottom drain valve (located around the bottom of your tank)

Open the valve and drain the tank