firstly, find someone who has a claybar (ask for a used one) - use that on the windscreen and make sure its clean all the way. Now check the wiper blades, when at rest they should sit "square" to the glass, if they are tilted or twisted or something (which some moron mechanics do for some reason), Fix that. The wipers will work correctly onwards.
The blades should be able to flex, if they are the metal cage type, make sure the assembly can flex, if not then fix that too, usually a drop of oil helps on the hinges of the blade skeleton. The last piece is that the blade mounting ear should not be floppy and loose. The blade should be able to rotate in one plane only on the mounting, otherwise the blade will chatter.