3 out of 4 teacher's tasks consists of two stages: the introduction and the exam. Before you gain access to exam, you'll have to get through the introduction.
The introduction: you need to the book which Hermione needs to finish the charms essay. It's simple: talk to Flitwick, run to Great Hall (you'll find the book there), speak with the schoolgirl, get back to Flitwick.
The exam: you cast various spells as fast as possible. (You won't pass the exam without Reducto.) There's additional hindrance: Harry don't know which item he should cast the spell on when there're 2 or more items nearby and some spells affect only certain items (for instance, Accio works only for the line near the fireplace and Incendio for wizard plaques). Getting the best degree might take a few tries. For me, the hardest part was casting Reparo on broken plates - Harry, like total idiot, tried to cast spell on a chair or stone bench, but never on the plates. I had to choose the right item manually, but there's a better way: Reparo is always after Reducto, so when you cast Reducto on the plates, you may start casting Reparo even before Flitwick tells you to do it. You'll save some time.
All you have to do in this case is a simple task. Speak with McGonagall, go to the tower of Divination and talk to students over there, get back to McGonagall. Done!
The introduction: to write an essay for professor Sprout, you're going to need Neville's book. You'll find it in Gryffindor Boys' Dormitory.
The exam: use Wingardium Leviosa on each mandrake to move it from broken pot to new one. Do it fast to get the best degree. Remember to use cursors on your keyboard to pick the right target.
The introduction: an essay about moonstone, 12 inches. :) You're going to need two things: a book from library and Hermione. The book is in restricted section, look at the bookshelves on the left side of room.
The exam: the rules are simple. You have to put the right potion into cauldron by using Wingardium Leviosa. You'll recognize which one is right through colors - color of the liquid in cauldron and color of the potion must match. To get the highest degree, you must do it 10 times. Be careful, one wrong move may ruin it all, especially in the end.