How do you get tartar buildup off of crowded teeth?

Dentist or hygienist. Only a dental professional can get the tarter off. It is pretty much impossible for a patient to scrape it off. After you get them cleaned, you definitely can keep it off with proper care, such as using a power toothbrush and flossing. Straightening the teeth will also make them easier to clean.
Brush and floss. Brush using a soft toothbrush at least 3 times a day, chew a sugarless gum and try to floss.
Hard to do. Not a do-it-yourself project. You will have to see your dentist or dental hygienist to have the hard accretions removed. They have the instruments and the skills to do it properly, above and below the gum line. Get your teeth straightened and they will be easier to keep clean.
Brushing. It is more difficult to keep your teeth clean when they are crowded and overlapped. Straightening your teeth will make this easier. In the meantime, regular cleanings with the dentist will help along with a great home routine of brushing and flossing.