As long as your turtle's shell is strong because of proper exposure to sun/heating lamps, then it's pretty sturdy. You don't have to worry too much about damaging it! =) The clorox answer is a good one, though I've used a scrub pad with the bleach on it rather than just pouring the bleach onto the turtle.
Don't hesitate to use a scrub pad or a toothbrush or something! There are treatments for algea as well, especially if it's been there a while and isn't just sloughing off like new algea will. But the treatments are probably more expensive.
The best thing you can do is make sure that your turtle has a good perch so it can become completely dry while under a heating lamp. This will kill the algea (which needs moisture) and make it easier to remove. Honestly, that will get rid of the algea (along with keeping the tank clean) better than anything else.
Good luck! =)