How would we change the two party system (please read details)?

Many of us don’t much like a two party system, but people only seem to try to change it at the last minute, during the elections with write-ins and last ditch third party candidates.

What can be done early on, in smaller elections, on the local and state levels to make a difference on a national scale, before we all get to the petty-bickering-before-the-big-election stage?

Honest question here, how can we revise/dismantle the two party system?