Basically, when you make a mistake, you scrape it off and rewrite it, unless it’s in one of God’s names, in which case you can’t scrape it off (because you mustn’t erase God’s Name) and must bury the sheet.
There are a number of different tools one can use to scrape off the mistake. Some people use an electric eraser (these go BZZZZZ and are awesomely efficient). Some use surgical scalpels. Some use X-acto knives. Some use glass shards. For all of these, you wait until the ink is good and dry, because otherwise it makes a perfectly dreadful mess.
There is a custom not to use implements made of ordinary metals on Torahs, because metals are used to make weapons, and that’s not a nice association for the Torah. That is why some people use glass shards, or gold-plated knives. Gold isn’t used to make weapons, it’s the metal of kingship, so that’s an exception. Surgical scalpels are also an exception, because they are used to save life, not to take life. An X-acto knife does not invalidate the Torah, but it doesn’t have the same homiletical associations.
Then you brush away the bits. You brush, not blow, because blowing makes the surface moist – huff onto a mirror, and imagine that getting all over the Torah.
Erasing usually leaves a rough sort of surface, so next you smooth the roughness. I use a burnishing tool made of bone. You want the surface to get as nearly as possible back to what it was before.
Then you score the guideline back in. All Torahs are written with guidelines; it’s not allowed to write Torah without guidelines even if you’re really good at keeping your lines straight.
Patches
If you tried all that on paper, you’d run into a pickle – the paper would get a hole in it. Parchment isn’t like that; generally you can scrape with no problem. However, sometimes you can’t, especially when water damage is involved. Water takes the ink straight through the parchment, so you can’t ever erase through to unaffected parchment.
Sometimes people spit when they talk (sorry. Horribly indelicate, I know), and the spit soaks all the way through, so you can’t erase the resulting mess. There is no solution but to cut the whole word out…
…and apply a clean piece of parchment to the back, with glue. Most glue is made sticky by boiling up bits of animals that even the dog-food factory doesn’t want – hooves and bones and things – so you can’t just use any old glue, because it might have bits of pigs or horses or something in it. And just you try phoning the glue company and trying to find out what’s in the glue. Believe me, they don’t want to tell you, even if you ask nicely. Like pulling hens’ teeth, I tell you. So you either use kosher glue, which you make by boiling up bits of kosher animals (ugh), or you use synthetic glue. You use archivist’s synthetic glue, because you don’t want to come back in ten years and find that the glue a) turned yellow or b) ate the parchment.
Then you write the new word. And you have to do it in that order. No writing the word first to make sure you get it right and then gluing it on.
Interesting point: patches ought to have round corners, because if you stick on something with pointy corners, it’s much more likely to peel off.
So why can’t you…
Those with their wits about them will ask at this point: If you can patch things you can’t scrape, why do you have to bury the sheet when you messed up God’s Name? Why can’t you just cut out the messed-up one and patch it?
And the answer is, because it’s not respectful. Partly it’s just not very nice (because we say so), and partly because patches are prone to falling off and getting lost on the floor, and you really don’t want that happening to God, as represented by God’s Name.