The screw securing the tap handle has sheard off. how can i remove it to get to the washer?

1. Open the dishwasher door and locate the screws on the inside of the door that hold the handle in place. There should be two screws, one at the top and one at the bottom.
2. Using a screwdriver, tighten both screws by turning them clockwise. If the screws are loose, this should fix the problem.
3. If the screws are tight and the handle is still loose, you may need to remove the handle and add a washer or two to create a tighter fit. To do this, remove the screws holding the handle in place and slide the handle off the studs.
4. Add a washer or two to each stud and slide the handle back on. Reattach the screws and test the handle to ensure it is now secure.
5. If these steps do not solve the problem, there may be an issue with the door itself,

this could be abad tap washer
a faulty loose pipe connection
or a faulty tap
turn of your water supply at the outside your house before proceeding
remove the handle on your tap then remove insert screw valve usually with a spanner or shifter
you should see a copper or plastic stem inside with a flat washer at the end which
http://www.videojug.com/film/how-to-fix-a-dripping-tap-bib-or-pillar
hope this helps

if your HOT label isn't attached to an end cap that can be removed to find the screw then look for a C-clip under the handle, pull it off then the handle will pull off

The screws into the tank to secure the top handle are self tapping, so if they will not tighten then yes the threads had stripped, you may be able to aquire some over sized screws to cure this, the saw has four rubber anti vibration mounts, and two bumper rubers either side of the tank to stop sideways movement, the later machine had a rubber around the right hand side of the top handle also to stop side ways movement, To change the rubbers you need to remove the starter cover, two of the securing screws also hold the l/h rubbers, remove the alloy chain catcher on the r/h side, and the cover plate top r/h side held with a single screw, the tank should now drop far enough to remove the rubbers, they are screw into the tank wit a self tapping screw on the back, you will need a special tool to remove them part no. 502510002, do not pull the tank too far down or you will stretch the fuel hose.

Probably what you need to do is change the cartridge. You will need a Moen cartridge puller to help with removal and reinstallation. You can get these and the cartridges at most hardware stores. Shut Off Water first, remove set screw that secures handle and carefully remove handle. You may have to tap lightly on rim of handle to free it. There is a retaining clip that holds cartridge in place, it will have a small round hole on top. Carefully remove clip using neddle nose pliers or perhaps ice pick inserted in hole to remove clip.Install puller as per instructions and tighten nut to remove cartridge. Install new cartridge andclip. put handle back on and install screw. I need to back up here and say that screw is normally located under moen insignia in middle of handle. Pry cover off with screw driver or knife blade to access screw. After you have cartridge, retaing clip and handle reinstalled turn water back on and check for leaks. Hope this helps. Thanks.

Turn off water at wall valve under sink. Turn on tap to ensure valve is shut off. Remove tap handle. Remove cap, collar or bushing holding shaft in place. Shaft may need to screwed out to remove. Replace washer on end of shaft, then re-install parts in reverse order.

There are several other methods.
Pop out a screw-cover cap on the end of the top of the handle.
Unscrew the base of the handle.
Unscrew the lever off the handle.
Pop out a small setscrew cover plug on the side of the handle under the lever. Hope this helps.

what brand valve, and model number?

without that...
some handles are screwed on, some are held on with allen set screws.
it all depends on the valve, and the model number.

After you remove the chrome collar and plastic collar washer (behind the faucet handle), pry the beauty plate off the wall. Turn off the house main water supply. Remove the four screws and washer holding the cartridge and valve stem in place. Save the metal washer under the four screws for use with the new cartridge. Replace the stem/cartridge assembly and secure with the saved metal washer and four screws. Reinstall beauty plate, collar & collar washer, then handle.

Is it a single handle or double handle faucet?
If it is a single:    1.  Remove handle via setscrew the side of the handle          (possibly under a decorative cap with the company name)    2.  Unscrew the packing nut holding the valve cartridge in    3.  Remove cartridge and access washers
For double handle    1.  Remove decorative cap on top of handle with a think screw driver.    2.  Remove handle and packing nut holding the valve stem in place    3.  Remove valve stem and body to access washers and o-rings.

Remember to turn water off at the source prior to doing any work. Replacement is just reverse of removal and don't forget to use a washer grease on all washers/o-rings when reassembling.