Well - there are two sides to avoiding tangles.
How you twist your hair - I make sure that my hair is combed out WELL, then I take two separate strands, and as I twist the strands around each other, I ALSO twist each strand. So - it's kind of a 'triple' twist.
Since I wear a twist out on Fridays, that allows my twist out to stay 'tight' because when I take the two strands apart, the individual strands are still 'twisted'.
When it comes time to untangle, since my twists are 'technically' already untwisted, I get my hair soaking wet, put in a nice thick conditioner, and patiently, patiently, patiently untangle and comb through my hair.
I've also noticed that if I oil my hair while it's in the twists - with either a scalp massage oil or some Oyin's Whipped Pudding, the tangles almost seem to FALL apart when it comes time to detangle.