The pedal chain placement alters when you're using a tube screamer for boosting, rather than just as a gain pedal. This means that you should have your tube screamer after any other overdrive or distortion pedals. You should still have it before any reverb, delay or modulation effects in most cases.
Should distortion go before or after overdrive?
Whether you want to put your overdrive or distortion first depends on what you want to boost the most. If you're looking for more of a distorted gain style, then put it after the overdrive. But if you want a subtler sound, then put your overdrive last and don't have your distortion pedal cranked up too much.
When should I use an overdrive pedal?
Complement. Players often use overdrive pedals to enhance or complement an already overdriven amplifier. One reason might be to boost the signal with a little bit of color. Another reason might be to fill in or focus specific frequencies for a sound that better cuts through the mix.