From my experience, this is caused from two issues which sort of exacerbate each other. First, your wipers aren't working as designed. Most likely, they have "gunk" on them which if cleaned off would help tremendously. The "gunk" on the wipers is getting smeared onto the windshield. As they continue to wipe, it just makes it worse. To fix this issue, you need to thoroughly clean both the wipers and the windshield. Windshield washer fluid itself isn't going to get it clean. Better fluid can help after these are clean.
Your wipers may or may not need to be replaced. Pull up the wiper arm and feel the blade with your thumb. If the rubber (term used generically) feels soft and supple, you can most likely clean them and they'll work just fine. The easiest way I've found to clean the wiper is, when at the fueling station which has a squeegee with a fluid soaked sponge on the back side, allow the wiper blade to ride on the sponge part while you move it the length of the wiper. If you do this a couple of times per wiper blade, it will do a great job of getting all the gunk off of it.
Conversely, I understand if you cut an apple or potato in 1/2, you can wipe this along the blade and it will clean it off as well. I've never done this, but understand it can do a good job.
Do either one of these things every couple of months and you'll find your wipers will be working much better. If the wipers are hard/still or have notches in them, it's time for replacements.
To clean your windshield, you're going to need a good cleaner. Household glass cleaner works very well. You can use Windex, but a better cleaner is the foaming type which comes in a metal can (I don't know what it's called). You'll need to supply some elbow grease, but this should get all the gunk off of there.
Once everything is clean, I usually use something like Rain-X, which is a hydrophobic and forces the water off of the windshield. In my experience, this really helps keep the windshield free of water and clear. I don't know if there are any other brands out there besides Rain-X, but I'm sure there must be others. There are also some additives you can put into your washer fluid which will retreat the windshield on a regular basis. This not only repels the water, it also helps to keep the windshield clean. You have to reapply it every so often, as it will get worn off.