In the Chamber Of Secrets, destroy paintings on the wall. You will open the painting and get 100 points for Gryffindor.
After returning from the Whomping Willow, head deep to your right when Professor Snape finishes scolding you. There, in a corner, you will find your first Notice Board Item. You can return it to the Notice Board before or after you go to the Restroom Shop the Weasley's set up, earning you the very first 10 points in the game, and possibly a Wizards Card.
As soon as you exit Flitwick's or McGonagall's spell challenge (not Lockhart's), the teacher gives you 40 house points. Save the game before leaving the room then quit. Load the game again and you will see yourself appear from the portrait hole, but this time everyone in the room is invisible. The invisible teacher will then give you another 40 house points. Save the game, and repeat this process as many times as desired to build up house points. Note: You can get over triple figures.
Go to the bulletin board in the common room and keep returning items to their owners. You will receive ten points each time you find and return an item.
On your first day at Hogwarts, you take a flying exam in Flying Class. To get extra house points, fail your exam the first time. Then, go back later in the year and take the exam again. If you get a better grade than before, Madam Hooch will give you more house points. You can keep on doing this when you are in desperate need for house points. Also, this will make it easier to defeat Slytherin for the House Cup.