How can I go from my couch to running a 5K in 3 months?

Basically, you are asking, how to go from not running at all to completing your first 5K.  It is best to first consult your doctor before starting any exercise program.  Make sure you invest in an excellent pair of running shoes, try a local running shoe store for advice.  Start off by measuring the time you are running.  Alternate days running and gradually increase the length of time being careful not to increase more than 10% per run.   Once you get up to 30 minutes of running every other day, start increasing the length of time running every fourth day by 10% again until you hit 45 minutes.  It is ok to walk if you feel you need to.  Then you will be 5K running race ready.