I have an elliptical at home and have been going steady at 45min 5x/week and would also like to incorporate some strength training.

I tried one of the 20 min workouts from Oprah/Dr Oz and found it a good beginner point for me.

Should I do this everyday? 3x/week? Should I do cardio before the 20 min workout or after?

Any advice would be greatly appreciated.

TGIF!!!

I think 2-3 days a week of strength training would be decent!

・Warmup (10~15 min)
・Stretch (5~10 min)
・Strengh training (20~30 min)
・Cardio (30~45 min)
・Cool down (10~15 min)
・Stretch (10~15 min)

I'm no professional trainer but this is the advice I've been receiving from trainers I know, my local gym, and articles I read.

Strength training before cardio helps you burn more calories during cardio. For max results you can even incorporate interval training (ex. 15 seconds max speed, 30-45 seconds normal speed, and repeat) into your cardio routine if you don't already.

Don't forget to stretch! A lot!! Strength training and any type of exercise in general works up your muscles, and relaxing them with stretches help improve your performance for the next time.