While you may not be able to do all forms of windshield repair by yourself, there are a couple that you can most definitely do: wiper replacements and wiper blade refills. Replacements are required when the blade actually breaks and refills are needed when the actual wiping edge becomes torn or develops gaps. Mostly they are quite straightforward but there are tricks which can save you many minutes of frustration and bafflement, and keep your stock of curses untapped.
Refills are cheaper but depending on what you're driving may not be an option. Best to check your car manual; sometimes it's worth asking at your auto parts shop as well because they may have kits that your manufacturer may not be aware of or would prefer that you don't know about. Once you have removed the old wiper blade, it's only a matter of slowly sliding the new one in from one end, carefully of course as you don't want to break it, and making sure that both ends are snug and don't extend past the end of the blade.
The three major forms of ordinary wipers — that's to say, the boring common kind that just go on the end of the wiper arms and don't spray water or anything, that just wipe the window — are: hook, side-lock, and bayonet. Your auto parts shop will have the guidebook for replacements: look up your car model and year, and take note if it gives you a different make for the driver's and passenger's side. Then try and find it. I have yet to discover a coherent method of displaying the things!
The instructions that come with the wiper blades invariably say "keep the arm and blade parallel to each other to keep the adaptor from detaching from the blade". You don't have to strain too hard to install the blades and with a judicious bit of angling you can do it much more easily without endangering the adaptor.
The blade will come with two adaptors — a one-piece lump and a hinged piece. The one-piece is for the hook type only.
The trick for all of these installations is the initial position of the replacement blade. In all cases hold it BELOW the arm in the operating position — with the blade facing the windshield.
Side-lock type: the wiper arm has a little pin sticking out at right angles. Take the hinged adaptor and slip it into the slot on top of the new blade assembly, big end first, so that it rests on the center pin. Slide the pin through the hole on the new blade. GENTLY bend the hinged portion of the adaptor into the slot, until it settles firmly into place.
Bayonet type: the wiper arm is completely straight and has a little dimple at the end. Slip the hinged adaptor into the slot on the top of the new blade, so that it rests on the centre pin. Close the hinged portion into the slot. Then push the new blade onto the arm, into the slot at the end of the adaptor, until you hear or feel the dimple snapping into place.
Hook type: make sure the old adaptor is removed from the hook: pry it out if necessary. Slide the adaptor in the new blade into the open end of the hook (it will only go in one way and that is obviously the correct way); once it's in a little way, you can hold the new blade at an angle so as to get more room to push the adaptor in the rest of the way.
There isn't much you can do with the old blades apart from recycling them. Sometimes it will be possible to pull the refill off the old blade but it's difficult.
More complicated replacements — when you have heated blades or water-emitting blades — are a difficult proposition.