What's 'enough' depends on your individual fitness level.
I've found great results from a 15-30 minute treadmill workout (done after your resistance training).
Here's an outline of a 6 week treadmill program you can try:
Week 1: Walk for 15 minutes on a level of speed and incline that challenge you but that you can still manage. As long as you are pushing yourself and are at a speed where you are power walking rather than jogging or running. Perform this 3-5 times in the week (depending on how your legs feel afterwards - if you are very sore then wait a couple of days until you feel that you can do it)
Week 2: Walk for 20 minutes, at the same incline and speed as week 1.
Week 3: Walk for 25 minutes, at the same incline and speed as weeks 1 and 2.
Week 4: Walk for 15 minutes, at the same speed but increase the Incline by one point.
Week 5: Walk for 20 minutes at the same speed and incline as week 4.
Week 6: Walk for 25 minutes at the same speed and incline as last week.
At this point, continue this pattern, or if you really want a challenge try something similar on the Stepper Machine.
Justin