The baskilisk has two lives, so don't get too excited when you beat him the first time. You will have a sword instead of a wand this time. Here's how you do it:
It would be best to back up as far to the surrounding wall as possible. Hold down the left mouse button and aim the red dot at the baskilisk's head. A yellow light will start growing around the sword. After a few seconds, release the button and immediately hold it down again. The light that grows around the sword will fire at the baskilisk and hurt it. Holding the button down again will create a new light around it. Repeat this until the baskilisk draws it's head back into the mouth of Salazar Slytherin. You've beaten the first life.
The baskilisk will come out of the four sewers on the ground. It always comes out of the one nearest to you, but it never comes out of the same sewer twice in a row. Hold down the left mouse button again, but don't release it yet. It will look to your right, then your right, and when it looks right at you, release the button. It will lose some life and retreat into the sewer again. But sometimes, when you hurt it, it will get angry and rock it's head from back to front, spitting out venom. Try to avoid the venom. Anyway, repeat until the baskilisk is dead.
The baskilisk's venom looks like purple ectoplasm. It will hurt you if you touch it. In the first life, if you get too close to the baskilisk, it can reach out and bite you. That takes away almost a whole stamina bolt, so stay back. Nothing ever tries to hurt Ginny, so don't waste your time trying to protect her.