What can I do to store and segregate my embroidery thread?
My personal floss storage method is floss bobbins.


via Michaels

These are typically available in any craft store that sells embroidery floss, in the same aisle as the floss. They're available in either thin plastic or cardstock, and typically have little notches at the top or bottom that lightly hold the floss in place as you wind it (and for storage). 

If you are feeling crafty, you can get free templates (e.g. here) to print and cut out your own -- either the more traditional "spool" profile, or more interesting/adorable shapes.


via Little White Whale

To keep the floss bobbins all stored together, there are a lot of possible storage methods. The above floss bobbin set has an included ring to hold the bobbins together. You can put them all in a plastic bag. You can build a custom box to hold them all in neat little rows. (The biggest limitation is your personal creativity.)


via Kat the Craft

Always write the floss color number on the tab so you know what color it is after the paper is gone! This does require a little up-front organizational work, but it's less effort than throwing out the tangled mass of thread and driving to the store for more :)